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6987db370dcd6b2e6b1afc905e9fb2ac7f31593d
schmorrow joined the u.s. navy's medical service corps
schmorrow joined the u.s. navy's medical service corps aerospace experimental psychology (aep) community in 1993 and was directly commissioned as a lieutenant (o-3). upon his accession schmorrow attended officer indoctrination school (ois, now officer development school) in newport rhode island. he was immediately made...
wikipedia
fce82d29183b48230b2584af814210034cb9aed5
schmorrow grew up in michigan. following high school,
schmorrow grew up in michigan. following high school, schmorrow enrolled in western michigan university (wmu) where he graduated in 1989 with degrees in both economics and psychology. after completing his undergraduate work, schmorrow enrolled in the graduate school at wmu, where he completed two master's degrees (expe...
wikipedia
b209473f9defb5374938bc4b4d20f3cfe6f11ef1
schmorrow was the recipient of the first leland
schmorrow was the recipient of the first leland s. kollmorgen spirit of innovation award presented by the human factors and ergonomics society (hfes) which was presented at the fourth augmented cognition international conference in baltimore on october 2, 2007 on may 29, 2008, at a ceremony at the pentagon, capt schmor...
wikipedia
363587ed305e8c3da8be0fe3bcb5b14ce1979ce4
he has previously served as the executive assistant
he has previously served as the executive assistant to the chief of naval research at the office of naval research. he was instrumental in expanding the field of augmented cognition as a darpa program manager. he was also a key developer of virtual environment technology as pm of the virte (virtual technologies and env...
wikipedia
d455403ba93706ba8b26904df8bf6ba078265d91
dylan schmorrow is an american scientist and retired
dylan schmorrow is an american scientist and retired united states defense official. he is currently the chief scientist at soar technology, inc.. he is a retired us navy captain, and served as the deputy director of the human performance, training, and biosystems research directorate at the office of the assistant sec...
wikipedia
b3e51957a52619686a66fa00e97df3ca08fc1351
economy-wide material flow accounts (ew-mfa) is a framework
economy-wide material flow accounts (ew-mfa) is a framework to compile statistics linking flows of materials from natural resources to a national economy. ew-mfa are descriptive statistics, in physical units such as tonnes per year. ew-mfa is consistent with the principles and system boundaries of the united nations sy...
wikipedia
dce8b2c96e9095be51d5a2da954998ac321edf9d
domestic processed output (dpo) measures the total weight
domestic processed output (dpo) measures the total weight of materials which are released back to the environment after having been used in the domestic economy. these flows occur at the processing, manufacturing, use, and final disposal stages of theproduction-consumption chain. included in dpo are emissions to air, i...
wikipedia
ba647cd9cabce68bf8cc318e08182cba3da5bd6d
net additions to stock (nas) measures the ‘physical
net additions to stock (nas) measures the ‘physical growth of the economy’, i.e. the quantity (weight) of new construction materials used in buildings and other infrastructure, and materials incorporated into new durable goods such as cars, industrial machinery, and household appliances. materials are added to the econ...
wikipedia
23e5901f099b106663290773e02a8354249d65b3
physical trade balance (ptb) equals physical imports minus
physical trade balance (ptb) equals physical imports minus physical exports. this means that in relation to monetary trade balances which is exports minus imports) the flows are the reverse. it measures the fact that in economies money and goods move in opposite direction. a physical trade surplus indicates a net impor...
wikipedia
a0ff08f082b9f277d1d8f7db3c93f98add95c54a
domestic material input (dmi) summarizes domestic extraction of
domestic material input (dmi) summarizes domestic extraction of resources and the imports, i.e. all materials which are of economic value and are used in production and consumption activities, except balancing items. dmi is not additive across countries. due to the inclusion of trade within the eu double counting would...
wikipedia
9278aa55094d0ced737f40d9b54b7b269e9b5b7a
direct material consumption (dmc) is defined as the
direct material consumption (dmc) is defined as the total amount of material directly used in an economy, i.e. it equals domestic extraction plus imports minus exports. dmc does not include upstream hidden flows related to imports and exports of raw materials and products.
wikipedia
18af74df4c0cd7769ffc7aef7b6f1ebac1da20c3
there is a link between the system of
there is a link between the system of integrated environmental and economic accounting (seea) and ew-mfa. statistics are based on the same principles (the residence principle of the sna) and thus become the ew-mfa a sub-component of the seea. the ew-mfa links the environment to the economy through the flows of material...
wikipedia
8ad3e908316563ca13a8651eee51995bb8bde0fe
in the european union between 2000 and 2007,
in the european union between 2000 and 2007, resource productivity increased by almost eight percent. resource productivity of the eu is expressed by the amount of gross domestic product (gdp) generated per unit of material consumed (domestic material consumption, see below), in other words gdp / dmc in euro per kg. th...
wikipedia
ceefa090df5cc00258db7eaf37939eb221424c0b
in principle, the statistics will show which countries
in principle, the statistics will show which countries are dependent on others for natural resources and which are major exporters of natural resources. the statistics also show if a countries production is sustainable, i.e. whether the economy of a country can produce more products using fewer natural resources.
wikipedia
7707a46d86dc246b751d9edd1abb600dd329d758
ew-mfa strives to produce a mass balance of
ew-mfa strives to produce a mass balance of material flows. it systematically categorises material input and output flows crossing the functional border between economy (technosphere, anthroposphere) and environment. mass balances are defined as "...on the first law of thermodynamics (called the law of conservation of ...
wikipedia
6195a1c343ff116479cce1dd60a639a6994c6cf3
the underlying definition of economy-wide material flow accounts
the underlying definition of economy-wide material flow accounts includes statistics on the overall material inputs into national economies, the changes of material stock within the economic system and the material outputs to other economies or to the environment. statistics on ew-mfa cover all solid, gaseous, and liqu...
wikipedia
5a667c04d94b6c13a0aa4be0f402381dcc9349a7
ew-mfa is consistent with the principles and system
ew-mfa is consistent with the principles and system boundaries of the united nations system of national accounts (sna) and follows the residence principle. this means that ew-mfa is also a part of the system of integrated environmental and economic accounting (seea).
wikipedia
a1814c9239f2c49d90bc5a1d13249b2a6bb5a4d7
elliott bridge is an old bridge over the
elliott bridge is an old bridge over the boral river in sirajganj, north-western bangladesh. the pillarless bridge is named after the lieutenant governor named charles alfred elliott. it cost 45 thousand takas to make it. it is one of the major attractions of sirajganj city.
wikipedia
039023023ac0986b6caa7fd439c35465ed4ebd32
the bridge is one of the sights of
the bridge is one of the sights of sirajganj city. in 1962, the construction of the sirajganj city protection dam on the jamuna made the mouth of a sluice gate at the baitara end of the katakhali river and the other mouth closed. in 2019, the re-excavation of the river happened by sirajganj water development board. the...
wikipedia
2b70ccec3e0eda0b9d2ca4db93f1d84b413342f5
the height of the bridge is 30 feet.
the height of the bridge is 30 feet. the bridge was raised and built without pillars so as not to disrupt the movement of large cargo ships plying the katakhali river. apart from this, standing on the bridge so that the view of sirajganj city could be seen was also another reason for building the bridge.
wikipedia
07d9f321098048e41e414555421bd63ffa18b486
it cost tk 45,000 to build the bridge
it cost tk 45,000 to build the bridge at that time. magistrate of pabna district julius gave a grant of tk 15,000 from the district board. the rest of the money was collected from donations from local zamindars and rich people.
wikipedia
dd028b6dbca89e3399465882942e4485086fc790
the hartland company built the bridge, designed by
the hartland company built the bridge, designed by stuart hartland who was a british engineer. charles alfred elliott, the then lieutenant governor of bengal laid its foundation stone on 6 august 1892. the bridge, named elliott bridge, is named after him. the bridge has since been renovated several times.
wikipedia
ab3786c03d4da6354712e8b2f4369c2678577ed6
the river boral or katakhali, which flows through
the river boral or katakhali, which flows through the town named sirajganj, divides the city into two parts, east and west. due to its connection with the river jamuna, the flow of water in this katakhali was much higher. so in 1892, the then sub-divisional officer bitson bell, planned to build a bridge to solve the tr...
wikipedia
146a9304fc29c745453daad801324368fbf9fd6a
elliott bridge (locally known as boropool) is an
elliott bridge (locally known as boropool) is an old bridge over the boral river in sirajganj, north-western bangladesh. the pillarless bridge is named after the lieutenant governor named charles alfred elliott. it cost 45 thousand takas to make it. it is one of the major attractions of sirajganj city.
wikipedia
7db1f4b1f241beb4d815a0a70198116f82a32b4d
enterprise modelling is the abstract representation, description and
enterprise modelling is the abstract representation, description and definition of the structure, processes, information and resources of an identifiable business, government body, or other large organization. it deals with the process of understanding an organization and improving its performance through creation and ...
wikipedia
593c318515513fef8e1c215755ae82fee94c7db7
the modelling of the enterprise and its environment
the modelling of the enterprise and its environment could facilitate the creation of enhanced understanding of the business domain and processes of the extended enterprise, and especially of the relations—both those that "hold the enterprise together" and those that extend across the boundaries of the enterprise. since...
wikipedia
3128fa96ed6f46b58bf10ac7ec77bf46a060f0b3
using ontologies in enterprise modelling offers several advantages.
using ontologies in enterprise modelling offers several advantages. ontologies ensure clarity, consistency, and structure to a model. they promote efficient model definition and analysis. generic enterprise ontologies allow for reusability of and automation of components. because ontologies are schemata or outlines, th...
wikipedia
29e494f416fbe387c6092e61b3be06c6b8b1de20
one common language with well articulated structure and
one common language with well articulated structure and vocabulary would enable the company to be more efficient in its operations. a common ontology will allow for effective communication, understanding and thus coordination among the various divisions of an enterprise. there are various kinds of ontologies used in nu...
wikipedia
b7d25a18255ea8b55e327e3c92555d317942aa25
ontology engineering or ontology building is a subfield
ontology engineering or ontology building is a subfield of knowledge engineering that studies the methods and methodologies for building ontologies. in the domain of enterprise architecture, an ontology is an outline or a schema used to structure objects, their attributes and relationships in a consistent manner. as in...
wikipedia
bdca8b8a2e3b5b8c60a1c1ed4375da3712ef997e
in general terms, economic models have two functions:
in general terms, economic models have two functions: first as a simplification of and abstraction from observed data, and second as a means of selection of data based on a paradigm of econometric study. the simplification is particularly important for economics given the enormous complexity of economic processes. this...
wikipedia
29f31054dd5d788ef9490dd9422b8c224918c113
economic modelling is the theoretical representation of economic
economic modelling is the theoretical representation of economic processes by a set of variables and a set of logical and/or quantitative relationships between them. the economic model is a simplified framework designed to illustrate complex processes, often but not always using mathematical techniques. frequently, eco...
wikipedia
241bbda4a246c0c42529efec603d61bb22434e30
a reference model in general is a model
a reference model in general is a model of something that embodies the basic goal or idea of something and can then be looked at as a reference for various purposes. a business reference model is a means to describe the business operations of an organization, independent of the organizational structure that perform the...
wikipedia
c2b4a2572136c0e936c0df9fc52c583af30e7f71
business reference modelling is the development of reference
business reference modelling is the development of reference models concentrating on the functional and organizational aspects of the core business of an enterprise, service organization or government agency. in enterprise engineering a business reference model is part of an enterprise architecture framework. this fram...
wikipedia
bc7fa3f1208f0b679fdc316b2418f68a17572f2e
in the context of software development a specific
in the context of software development a specific field of enterprise engineering has emerged, which deals with the modelling and integration of various organizational and technical parts of business processes. in the context of information systems development it has been the area of activity in the organization of the...
wikipedia
52c3e91b8c25c8e706375ec03bfe2ebc5b2fa59c
in the field of engineering a more general
in the field of engineering a more general enterprise engineering emerged, defined as the application of engineering principals to the management of enterprises. it encompasses the application of knowledge, principles, and disciplines related to the analysis, design, implementation and operation of all elements associa...
wikipedia
b8f2193bdf941a993a868151cb2d48f244ac6c3d
enterprise engineering is the discipline concerning the design
enterprise engineering is the discipline concerning the design and the engineering of enterprises, regarding both their business and organization. in theory and practice two types of enterprise engineering has emerged. a more general connected to engineering and the management of enterprises, and a more specific relate...
wikipedia
effa4b8340c2ea9725a2995eca2a9901b21c82c1
the rm-odp reference model identifies enterprise modelling as
the rm-odp reference model identifies enterprise modelling as providing one of the five viewpoints of an open distributed system. note that such a system need not be a modern-day it system: a banking clearing house in the 19th century may be used as an example ().
wikipedia
6de5a99713e986804aea7b3642354b8d48821956
change management programs are typically involved to put
change management programs are typically involved to put the improved business processes into practice. with advances in technology from large platform vendors, the vision of business process modelling models becoming fully executable (and capable of simulations and round-trip engineering) is coming closer to reality e...
wikipedia
640d3c2b4e97ba9885d9a29dd3ec2597b94d6f52
business process modelling, not to be confused with
business process modelling, not to be confused with the wider business process management (bpm) discipline, is the activity of representing processes of an enterprise, so that the current ("as is") process may be analyzed and improved in future ("to be"). business process modelling is typically performed by business an...
wikipedia
c764a9e8f4d101b88cde34fc5b346c67d93d355b
the figure illustrates the way data models are
the figure illustrates the way data models are developed and used today. a conceptual data model is developed based on the data requirements for the application that is being developed, perhaps in the context of an activity model. the data model will normally consist of entity types, attributes, relationships, integrit...
wikipedia
ef0f269dd03678cba98f01e55fefa25ca2848017
data modelling is the process of creating a
data modelling is the process of creating a data model by applying formal data model descriptions using data modelling techniques. data modelling is a technique for defining business requirements for a database. it is sometimes called database modelling because a data model is eventually implemented in a database.
wikipedia
8696c35ed6b43d744a79aa518d908f1189d1d962
now, with these symbols, a process can be
now, with these symbols, a process can be represented as a network of these symbols. this decomposed process is a dfd, data flow diagram. in dynamic enterprise modeling, for example, a division is made in the control model, function model, process model and organizational model.
wikipedia
75710a9d11845889a2a79e27f59934e6b4fe4d42
a functional modelling perspective concentrates on describing the
a functional modelling perspective concentrates on describing the dynamic process. the main concept in this modelling perspective is the process, this could be a function, transformation, activity, action, task etc. a well-known example of a modelling language employing this perspective is data flow diagrams. the persp...
wikipedia
eaf63213e33a9f2a5de0528b4e10eff4454a0d3a
a function model, also called an activity model
a function model, also called an activity model or process model, is a graphical representation of an enterprise 's function within a defined scope. the purposes of the function model are: to describe the functions and processes, assist with discovery of information needs, help identify opportunities, and establish a b...
wikipedia
ae66d2217736302cb0f1cb674ed26d250feb10c3
in a two-volume set entitled the managerial cybernetics
in a two-volume set entitled the managerial cybernetics of organization stafford beer introduced a model of the enterprise, the viable system model (vsm). volume 2, the heart of enterprise, analyzed the vsm as a recursive organization of five systems: system one (s1) through system five (s5). beer's model differs from ...
wikipedia
92955594319bdea3d35c9f562d5af6042257ab78
according to fox and gruninger (1998) from "a
according to fox and gruninger (1998) from "a design perspective, an enterprise model should provide the language used to explicitly define an enterprise... from an operations perspective, the enterprise model must be able to represent what is planned, what might happen, and what has happened. it must supply the inform...
wikipedia
770234538844d2d589af96fd1ac0d7546977c86e
an enterprise model is a representation of the
an enterprise model is a representation of the structure, activities, processes, information, resources, people, behavior, goals, and constraints of a business, government, or other enterprises. thomas naylor (1970) defined a (simulation) model as "an attempt to describe the interrelationships among a corporation's fin...
wikipedia
c052ad1153957bf35cc4653f32054d705ff43488
these second generation of methods were activity-based methods
these second generation of methods were activity-based methods which have been surpassed on the one hand by process-centred modelling methods developed in the 1990s such as architecture of integrated information systems (aris), cimosa and integrated enterprise modeling (iem). and on the other hand by object-oriented me...
wikipedia
f62a720cc9162492d609769a065a207f2770a50f
the first methods dealing with enterprise modelling emerged
the first methods dealing with enterprise modelling emerged in the 1970s. they were the entity-relationship approach of peter chen (1976) and sadt of douglas t. ross (1977), the one concentrate on the information view and the other on the function view of business entities. these first methods have been followed end 19...
wikipedia
5c4298156930ad1cf6c2ca706e7552ebc6d29fa9
enterprise modelling has its roots in systems modelling
enterprise modelling has its roots in systems modelling and especially information systems modelling. one of the earliest pioneering works in modelling information systems was done by young and kent (1958), who argued for "a precise and abstract way of specifying the informational and time characteristics of a data pro...
wikipedia
f57ca82327aa818241da6abda781d790fe80069d
the basic idea of enterprise modelling according to
the basic idea of enterprise modelling according to ulrich frank is "to offer different views on an enterprise, thereby providing a medium to foster dialogues between various stakeholders - both in academia and in practice. for this purpose they include abstractions suitable for strategic planning, organisational (re-)...
wikipedia
d06dcb12749f8753cd4fbe50a73ccea7cd0f2265
the term "enterprise model" is used in industry
the term "enterprise model" is used in industry to represent differing enterprise representations, with no real standardized definition. due to the complexity of enterprise organizations, a vast number of differing enterprise modelling approaches have been pursued across industry and academia. enterprise modelling cons...
wikipedia
a0e51f69b9d60c7b615a1440b6a3188a73f100e3
enterprise modelling is the process of building models
enterprise modelling is the process of building models of whole or part of an enterprise with process models, data models, resource models and/or new ontologies etc. it is based on knowledge about the enterprise, previous models and/or reference models as well as domain ontologies using model representation languages. ...
wikipedia
de1a8ab9c5df12c514542836731a64177736585d
it deals with the process of understanding an
it deals with the process of understanding an organization and improving its performance through creation and analysis of enterprise models. this includes the modelling of the relevant business domain (usually relatively stable), business processes (usually more volatile), and uses of information technology within the ...
wikipedia
2e48c94a2b9d05f9cb58003961a27f406b1a2898
ernest edward leslie dixon was a british geologist,
ernest edward leslie dixon was a british geologist, who worked for the british geological survey for his whole career. he was best known for his geological investigations in south wales, and was awarded the murchison medal of the geological society of london in 1936.
wikipedia
8b8ed7ba40053f75bc6eb58184a1c57889d0a9be
dixon was awarded the murchison fund of the
dixon was awarded the murchison fund of the geological society of london in 1913, and the murchison medal in 1936. he was also awarded the foulerton award of the geologists' association in 1939.
wikipedia
e317fc1ef2282e495b73507aa5a7e12ce4647d18
dixon grew up in london, and went to
dixon grew up in london, and went to school at the city of london school. he studied geology at the royal college of science, graduating with a first class bsc. he joined the british geological survey in 1899, and worked with the survey until he retired in 1938. in his time with the survey, dixon published many papers,...
wikipedia
2e48c94a2b9d05f9cb58003961a27f406b1a2898
ernest edward leslie dixon was a british geologist,
ernest edward leslie dixon was a british geologist, who worked for the british geological survey for his whole career. he was best known for his geological investigations in south wales, and was awarded the murchison medal of the geological society of london in 1936.
wikipedia
3205e35f37552e234564c8b79ccae736f9152972
in coding theory, the bose–chaudhuri–hocquenghem codes form a
in coding theory, the bose–chaudhuri–hocquenghem codes form a class of cyclic error-correcting codes that are constructed using polynomials over a finite field. bch codes were invented in 1959 by french mathematician alexis hocquenghem, and independently in 1960 by raj chandra bose and d.k. ray-chaudhuri. the name bose...
wikipedia
ffe2a56eec5ffd436d8ea3fb3f47b10f2e2bb674
let us look for error values using formula
let us look for error values using formula e j = − Ω (α − i j) / Ξ ′ (α − i j), {\displaystyle e_{j}=-\omega \left(\alpha ^{-i_{j}}\right)/\xi '\left(\alpha ^{-i_{j}}\right),} where α − i j {\displaystyle \alpha ^{-i_{j}}} are roots of polynomial Ξ (x). {\displaystyle \xi (x).}
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02edebb43ac00345473b52007a394991e8e2e343
let Λ (x) = α 3 + α
let Λ (x) = α 3 + α 1 x. {\displaystyle \lambda (x)=\alpha ^{3}+\alpha ^{1}x.} don't worry that λ 0 ≠ 1. {\displaystyle \lambda _{0}\neq 1.} the root of Λ (x) {\displaystyle \lambda (x)} is α 3 − 1. {\displaystyle \alpha ^{3-1}.}
wikipedia
207623659f6567082452cd2c6c01fd3a08c62b8f
again, replace the unreadable characters by zeros while
again, replace the unreadable characters by zeros while creating the polynomial reflecting their positions Γ (x) = (α 8 x − 1) (α 11 x − 1). {\displaystyle \gamma (x)=\left(\alpha ^{8}x-1\right)\left(\alpha ^{11}x-1\right).} compute the syndromes s 1 = α 4, s 2 = α − 7, s 3 = α 1, s 4 = α 1, s 5 = α 0, {\displaystyle s...
wikipedia
7ff1460d161c910b34cdf4f2d8e844dc1a6b783f
where α − i j {\displaystyle \alpha ^{-i_{j}}}
where α − i j {\displaystyle \alpha ^{-i_{j}}} are roots of Ξ (x). {\displaystyle \xi (x).} Ξ ′ (x) = α 2 x 2. {\displaystyle \xi '(x)=\alpha ^{2}x^{2}.} we get
wikipedia
7465825994896a80f29549da0d14138d332dbdb7
let Λ (x) = α 3 + α
let Λ (x) = α 3 + α − 5 x + α 6 x 2. {\displaystyle \lambda (x)=\alpha ^{3}+\alpha ^{-5}x+\alpha ^{6}x^{2}.} don't worry that λ 0 ≠ 1. {\displaystyle \lambda _{0}\neq 1.} find by brute force a root of Λ. {\displaystyle \lambda.} the roots are α 2, {\displaystyle \alpha ^{2},} and α 10 {\displaystyle \alpha ^{10}} (afte...
wikipedia
8bdc86613e9b1ae23a57d8bf573adaf86210e10e
suppose the same scenario, but the received word
suppose the same scenario, but the received word has two unreadable characters. we replace the unreadable characters by zeros while creating the polynomial reflecting their positions Γ (x) = (α 8 x − 1) (α 11 x − 1). {\displaystyle \gamma (x)=\left(\alpha ^{8}x-1\right)\left(\alpha ^{11}x-1\right).} we compute the synd...
wikipedia
2a42c5bd77f04e9974ac79e4a49fda4b40049fa7
due to the zero row, s is singular,
due to the zero row, s is singular, which is no surprise since only two errors were introduced into the codeword.however, the upper-left corner of the matrix is identical to, which gives rise to the solution λ 2 = 1000, {\displaystyle \lambda _{2}=1000,} λ 1 = 1011. {\displaystyle \lambda _{1}=1011.} the resulting erro...
wikipedia
a6d8f05f1aed30f423c8f0ea28a11f9e9f06d912
in order to correct the errors, first calculate
in order to correct the errors, first calculate the syndromes. taking α = 0010, {\displaystyle \alpha =0010,} we have s 1 = r (α 1) = 1011, {\displaystyle s_{1}=r(\alpha ^{1})=1011,} s 2 = 1001, {\displaystyle s_{2}=1001,} s 3 = 1011, {\displaystyle s_{3}=1011,} s 4 = 1101, {\displaystyle s_{4}=1101,} s 5 = 0001, {\dis...
wikipedia
b43511bf077e606f49ecce41628bc48521a9913c
consider a bch code in gf(2) with d
consider a bch code in gf(2) with d = 7 {\displaystyle d=7} and g (x) = x 10 + x 8 + x 5 + x 4 + x 2 + x + 1 {\displaystyle g(x)=x^{10}+x^{8}+x^{5}+x^{4}+x^{2}+x+1}. (this is used in qr codes.) let the message to be transmitted be, or in polynomial notation, m (x) = x 4 + x 3 + x + 1. {\displaystyle m(x)=x^{4}+x^{3}+x+...
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3f84c03f584e547ec379fa33f175e0feb028df17
it could happen that the euclidean algorithm finds
it could happen that the euclidean algorithm finds Λ (x) {\displaystyle \lambda (x)} of degree higher than 1 2 (d − 1 − k) {\displaystyle {\tfrac {1}{2}}(d-1-k)} having number of different roots equal to its degree, where the fourney formula would be able to correct errors in all its roots, anyway correcting such many ...
wikipedia
98a1bfe321eacbfad7c75900599eb2958a129b0b
in euclidean algorithm, we try to correct at
in euclidean algorithm, we try to correct at most 1 2 (d − 1 − k) {\displaystyle {\tfrac {1}{2}}(d-1-k)} errors (on readable positions), because with bigger error count there could be more codewords in the same distance from the received word. therefore, for Λ (x) {\displaystyle \lambda (x)} we are looking for, the equ...
wikipedia
2b153fe824cca9cc09eaf5bdf8294b810712f03c
one could consider looking for error positions from
one could consider looking for error positions from the point of view of eliminating influence of given positions similarly as for unreadable characters. if we found v {\displaystyle v} positions such that eliminating their influence leads to obtaining set of syndromes consisting of all zeros, than there exists error v...
wikipedia
2e3237333628bbf1ab514246e5874ac39a9490eb
after replacement of s (x) {\displaystyle s(x)} by
after replacement of s (x) {\displaystyle s(x)} by s (x) Γ (x) {\displaystyle s(x)\gamma (x)}, one would require equation for coefficients near powers k, ⋯, d − 2. {\displaystyle k,\cdots,d-2.}
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7cd05bfd7a5a60537c8efa4063ca56c84ee17db8
in polynomial formulation, the replacement of syndromes set
in polynomial formulation, the replacement of syndromes set { s c, ⋯, s c + d − 2 } {\displaystyle \{s_{c},\cdots,s_{c+d-2}\}} by syndromes set { t c, ⋯, t c + d − 3 } {\displaystyle \{t_{c},\cdots,t_{c+d-3}\}} leads to
wikipedia
aee19b5945724c5a5d5fe230f950f1adb7b3769f
the same way the original set of syndromes
the same way the original set of syndromes restricted the error vector e j. {\displaystyle e_{j}.} except the coordinate k 1, {\displaystyle k_{1},} where we have f k 1 = 0, {\displaystyle f_{k_{1}}=0,} an f j {\displaystyle f_{j}} is zero, if e j = 0. {\displaystyle e_{j}=0.} for the goal of locating error positions w...
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7b546d129505de536c0da7e256f6c730bf6e5860
suppose there is unreadable letter on position k
suppose there is unreadable letter on position k 1, {\displaystyle k_{1},} we could replace set of syndromes { s c, ⋯, s c + d − 2 } {\displaystyle \{s_{c},\cdots,s_{c+d-2}\}} by set of syndromes { t c, ⋯, t c + d − 3 } {\displaystyle \{t_{c},\cdots,t_{c+d-3}\}} defined by equation t i = α k 1 s i − s i + 1. {\displays...
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3325132acc8f81145f5b717e58349c3193a6ee48
the goal is to find a codeword which
the goal is to find a codeword which differs from the received word minimally as possible on readable positions. when expressing the received word as a sum of nearest codeword and error word, we are trying to find error word with minimal number of non-zeros on readable positions. syndrom s i {\displaystyle s_{i}} restr...
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4316779900188b5be3ea3ccb46ec6e36280a380a
the main advantage of the algorithm is that
the main advantage of the algorithm is that it meanwhile computes Ω (x) = s (x) Ξ (x) mod x d − 1 = r (x) {\displaystyle \omega (x)=s(x)\xi (x){\bmod {x}}^{d-1}=r(x)} required in the forney formula.
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3af2a7357cda3eb6440e3d487775cefd41861263
defining Ξ (x) = a (x) Γ (x)
defining Ξ (x) = a (x) Γ (x) {\displaystyle \xi (x)=a(x)\gamma (x)} and using Ξ {\displaystyle \xi } on the place of Λ (x) {\displaystyle \lambda (x)} in the fourney formula will give us error values.
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8ecd9ef0c556008db4bbcfe29df446acebc6fb1b
let us run extended euclidean algorithm for locating
let us run extended euclidean algorithm for locating least common divisor of polynomials s (x) Γ (x) {\displaystyle s(x)\gamma (x)} and x d − 1. {\displaystyle x^{d-1}.} the goal is not to find the least common divisor, but a polynomial r (x) {\displaystyle r(x)} of degree at most ⌊ (d + k − 3) / 2 ⌋ {\displaystyle \lf...
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ec1169c69061b622dee3c6ead7f7fc8fffc843cd
as we have already defined for the forney
as we have already defined for the forney formula let s (x) = ∑ i = 0 d − 2 s c + i x i. {\displaystyle s(x)=\sum _{i=0}^{d-2}s_{c+i}x^{i}.}
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6879f51deb8d57369a444a6a9fee1cf0684712f1
let k 1,..., k k {\displaystyle k_{1},...,k_{k}} be
let k 1,..., k k {\displaystyle k_{1},...,k_{k}} be positions of unreadable characters. one creates polynomial localising these positions Γ (x) = ∏ i = 1 k (x α k i − 1). {\displaystyle \gamma (x)=\prod _{i=1}^{k}\left(x\alpha ^{k_{i}}-1\right).} set values on unreadable positions to 0 and compute the syndromes.
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6aee942d1a75e2ed34f2e109bb164a4b3195fe43
to get e k {\displaystyle e_{k}} we just
to get e k {\displaystyle e_{k}} we just should get rid of the product. we could compute the product directly from already computed roots α − i j {\displaystyle \alpha ^{-i_{j}}} of Λ, {\displaystyle \lambda,} but we could use simpler form.
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26fcf6760baea661e5fee42d3f8cf93f31e65aac
we want to compute unknowns e j, {\displaystyle
we want to compute unknowns e j, {\displaystyle e_{j},} and we could simplify the context by removing the (x α i j) d − 1 {\displaystyle \left(x\alpha ^{i_{j}}\right)^{d-1}} terms. this leads to the error evaluator polynomial
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e612c5149b09fe485ae78d2ee46780e2c5f38a3b
consider s (x) Λ (x), {\displaystyle s(x)\lambda (x),}
consider s (x) Λ (x), {\displaystyle s(x)\lambda (x),} and for the sake of simplicity suppose λ k = 0 {\displaystyle \lambda _{k}=0} for k > v, {\displaystyle k>v,} and s k = 0 {\displaystyle s_{k}=0} for k > c + d − 2. {\displaystyle k>c+d-2.} then
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3b704e1f90be24ffd8732db40a9601407bcff0b9
for the case of binary bch, (with all
for the case of binary bch, (with all characters readable) this is trivial; just flip the bits for the received word at these positions, and we have the corrected code word. in the more general case, the error weights e j {\displaystyle e_{j}} can be determined by solving the linear system
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f8a015d156f2c3a7848df6c59e82e28956a6f00f
now that you have the Λ (x) {\displaystyle
now that you have the Λ (x) {\displaystyle \lambda (x)} polynomial, its roots can be found in the form Λ (x) = (α i 1 x − 1) (α i 2 x − 1) ⋯ (α i v x − 1) {\displaystyle \lambda (x)=\left(\alpha ^{i_{1}}x-1\right)\left(\alpha ^{i_{2}}x-1\right)\cdots \left(\alpha ^{i_{v}}x-1\right)} by brute force for example using the...
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9ea70226a833b437661558d1d6f2d033fe134c93
peterson's algorithm is the step 2 of the
peterson's algorithm is the step 2 of the generalized bch decoding procedure. peterson's algorithm is used to calculate the error locator polynomial coefficients λ 1, λ 2, …, λ v {\displaystyle \lambda _{1},\lambda _{2},\dots,\lambda _{v}} of a polynomial
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b4113747c9702dbfcab05bb9127774c042ae7687
if there is a single error, write this
if there is a single error, write this as e (x) = e x i, {\displaystyle e(x)=e\,x^{i},} where i {\displaystyle i} is the location of the error and e {\displaystyle e} is its magnitude. then the first two syndromes are
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9d53a790751f1b8e702c1f447786a134ddffaabb
since α j {\displaystyle \alpha ^{j}} are the
since α j {\displaystyle \alpha ^{j}} are the zeros of g (x), {\displaystyle g(x),} of which c (x) {\displaystyle c(x)} is a multiple, c (α j) = 0. {\displaystyle c\left(\alpha ^{j}\right)=0.} examining the syndrome values thus isolates the error vector so one can begin to solve for it.
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2e97a234f17036e8989fd94c19233ed3a796291d
the received vector r {\displaystyle r} is the
the received vector r {\displaystyle r} is the sum of the correct codeword c {\displaystyle c} and an unknown error vector e. {\displaystyle e.} the syndrome values are formed by considering r {\displaystyle r} as a polynomial and evaluating it at α c, …, α c + d − 2. {\displaystyle \alpha ^{c},\ldots,\alpha ^{c+d-2}.}...
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802dca9bd19028a2046e2f9db01964f932bfe4df
during some of these steps, the decoding algorithm
during some of these steps, the decoding algorithm may determine that the received vector has too many errors and cannot be corrected. for example, if an appropriate value of t is not found, then the correction would fail. in a truncated (not primitive) code, an error location may be out of range. if the received vecto...
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3e97932218f4931f4df25d319489fd0467a94b10
over g f (2) {\displaystyle gf(2)} (i.e. with
over g f (2) {\displaystyle gf(2)} (i.e. with binary bch codes), this process is indistinguishable from appending a cyclic redundancy check, and if a systematic binary bch code is used only for error-detection purposes, we see that bch codes are just a generalization of the mathematics of cyclic redundancy checks.
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93e09e659b52486726915eae44deac4898383d34
here, we see that q (x) g (x)
here, we see that q (x) g (x) {\displaystyle q(x)g(x)} is a valid codeword. as r (x) {\displaystyle r(x)} is always of degree less than n − k {\displaystyle n-k} (which is the degree of g (x) {\displaystyle g(x)}), we can safely subtract it from p (x) x n − k {\displaystyle p(x)x^{n-k}} without altering any of the mess...
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d2856162ebb691080d7a108db9819118706ab739
this encoding method leverages the fact that subtracting
this encoding method leverages the fact that subtracting the remainder from a dividend results in a multiple of the divisor. hence, if we take our message polynomial p (x) {\displaystyle p(x)} as before and multiply it by x n − k {\displaystyle x^{n-k}} (to "shift" the message out of the way of the remainder), we can t...
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4be3163402492a76ba07da8e7c75de61d8efcb43
a systematic code is one in which the
a systematic code is one in which the message appears verbatim somewhere within the codeword. therefore, systematic bch encoding involves first embedding the message polynomial within the codeword polynomial, and then adjusting the coefficients of the remaining (non-message) terms to ensure that s (x) {\displaystyle s(...
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fa2e6f17282e23e6605515f73bae216e1a00aeea
the receiver can use these bits as coefficients
the receiver can use these bits as coefficients in s (x) {\displaystyle s(x)} and, after error-correction to ensure a valid codeword, can recompute p (x) = s (x) / g (x) {\displaystyle p(x)=s(x)/g(x)}
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26567c537862cb3597842ad08a7c0bcf1966ee6f
as an example, consider the generator polynomial g
as an example, consider the generator polynomial g (x) = x 10 + x 9 + x 8 + x 6 + x 5 + x 3 + 1 {\displaystyle g(x)=x^{10}+x^{9}+x^{8}+x^{6}+x^{5}+x^{3}+1}, chosen for use in the (31, 21) binary bch code used by pocsag and others. to encode the 21-bit message {101101110111101111101}, we first represent it as a polynomi...
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79021430818fef5e6c44b3c11bca7f33fa62b0ad
the bch code itself is not prescriptive about
the bch code itself is not prescriptive about the meaning of the coefficients of the polynomial; conceptually, a bch decoding algorithm's sole concern is to find the valid codeword with the minimal hamming distance to the received codeword. therefore, the bch code may be implemented either as a systematic code or not, ...
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203d59cfc9391ab8c542a76c38173ad1881c45fa
the generator polynomial of a bch code has
the generator polynomial of a bch code has degree at most (d − 1) m {\displaystyle (d-1)m}. moreover, if q = 2 {\displaystyle q=2} and c = 1 {\displaystyle c=1}, the generator polynomial has degree at most d m / 2 {\displaystyle dm/2}.
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4814741516f77a85a5e137183da3b24a866a2473
the generator polynomial g (x) {\displaystyle g(x)} of
the generator polynomial g (x) {\displaystyle g(x)} of a bch code has coefficients from g f (q). {\displaystyle \mathrm {gf} (q).} in general, a cyclic code over g f (q p) {\displaystyle \mathrm {gf} (q^{p})} with g (x) {\displaystyle g(x)} as the generator polynomial is called a bch code over g f (q p). {\displaystyle...
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