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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).} | wikipedia |
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+... | wikipedia |
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.} | wikipedia |
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... | wikipedia |
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... | wikipedia |
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... | wikipedia |
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. | wikipedia |
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. | wikipedia |
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... | wikipedia |
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}.} | wikipedia |
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. | wikipedia |
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. | wikipedia |
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 | wikipedia |
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 | wikipedia |
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 | wikipedia |
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... | wikipedia |
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 | wikipedia |
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 | wikipedia |
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. | wikipedia |
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}.}... | wikipedia |
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... | wikipedia |
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. | wikipedia |
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... | wikipedia |
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... | wikipedia |
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(... | wikipedia |
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)} | wikipedia |
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... | wikipedia |
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, ... | wikipedia |
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}. | wikipedia |
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... | wikipedia |
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