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id stringlengths 40 40	title stringlengths 15 120	text stringlengths 41 3.14k	source stringclasses 2 values
8209c7ea9072f551989edf6dff840ce5b48de1a1	note: if n = q m − 1	note: if n = q m − 1 {\displaystyle n=q^{m}-1} as in the simplified definition, then g c d (n, q) {\displaystyle {\rm {gcd}}(n,q)} is 1, and the order of q {\displaystyle q} modulo n {\displaystyle n} is m. {\displaystyle m.} therefore, the simplified definition is indeed a special case of the general one.	wikipedia
113b224c3d6d720b709121acdfef8cf1b39673fd	as before, let α {\displaystyle \alpha } be	as before, let α {\displaystyle \alpha } be a primitive n {\displaystyle n} th root of unity in g f (q m), {\displaystyle gf(q^{m}),} and let m i (x) {\displaystyle m_{i}(x)} be the minimal polynomial over g f (q) {\displaystyle gf(q)} of α i {\displaystyle \alpha ^{i}} for all i. {\displaystyle i.} the generator polyn...	wikipedia
f589a4691a01c4291b9e4504b8b2c8c0f6b85309	definition. fix a finite field g f (q),	definition. fix a finite field g f (q), {\displaystyle gf(q),} where q {\displaystyle q} is a prime power. choose positive integers m, n, d, c {\displaystyle m,n,d,c} such that 2 ≤ d ≤ n, {\displaystyle 2\leq d\leq n,} g c d (n, q) = 1, {\displaystyle {\rm {gcd}}(n,q)=1,} and m {\displaystyle m} is the multiplicative o...	wikipedia
cff4f3baf5bba17cc9f84f005f06ffbdfbc86604	second, the consecutive roots of the generator polynomial	second, the consecutive roots of the generator polynomial may run from α c, …, α c + d − 2 {\displaystyle \alpha ^{c},\ldots,\alpha ^{c+d-2}} instead of α, …, α d − 1. {\displaystyle \alpha,\ldots,\alpha ^{d-1}.}	wikipedia
2863629ddf21f66c205d78a521b4666c9cfd3433	first, the requirement that α {\displaystyle \alpha }	first, the requirement that α {\displaystyle \alpha } be a primitive element of g f (q m) {\displaystyle \mathrm {gf} (q^{m})} can be relaxed. by relaxing this requirement, the code length changes from q m − 1 {\displaystyle q^{m}-1} to o r d (α), {\displaystyle \mathrm {ord} (\alpha),} the order of the element α. {\di...	wikipedia
87b3c16322def9fa21e539e786e7c20c4d6d4527	this code has minimal hamming distance 15 and	this code has minimal hamming distance 15 and corrects 7 errors. it has 1 data bit and 14 checksum bits. it is also denoted as: (15, 1) bch code. in fact, this code has only two codewords: 000000000000000 and 111111111111111 (a trivial repetition code).	wikipedia
6c0d2938bfd4ace47faed05700436f1a43db6261	it has minimal hamming distance at least 7	it has minimal hamming distance at least 7 and corrects up to three errors. since the generator polynomial is of degree 10, this code has 5 data bits and 10 checksum bits. it is also denoted as: (15, 5) bch code. (this particular generator polynomial has a real-world application, in the "format information" of the qr c...	wikipedia
0eaca6642f16bdc9d2bc9fb37d052b82b0b3e902	it has minimal hamming distance at least 5	it has minimal hamming distance at least 5 and corrects up to two errors. since the generator polynomial is of degree 8, this code has 7 data bits and 8 checksum bits. it is also denoted as: (15, 7) bch code.	wikipedia
feb0100bd4396088343b91876b58f259e308c6fe	it has minimal hamming distance at least 3	it has minimal hamming distance at least 3 and corrects up to one error. since the generator polynomial is of degree 4, this code has 11 data bits and 4 checksum bits. it is also denoted as: (15, 11) bch code.	wikipedia
d31b2fde4f4531e51c081d16036dd02630cc9b6d	let q = 2 and m = 4	let q = 2 and m = 4 (therefore n = 15). we will consider different values of d for gf(16) = gf(2) based on the reducing polynomial z + z + 1, using primitive element α (z) = z. there are fourteen minimum polynomials m (x) with coefficients in gf(2) satisfying	wikipedia
4988c4adaea3359df3e657da6b4a04b16b564c74	let α be a primitive element of gf(q).for	let α be a primitive element of gf(q).for any positive integer i, let m (x) be the minimal polynomial with coefficients in gf(q) of α.the generator polynomial of the bch code is defined as the least common multiple g (x) = lcm(m (x),…, m (x)).it can be seen that g (x) is a polynomial with coefficients in gf(q) and divi...	wikipedia
8ebef70673dc2887b8d700c253527084a38ede9c	given a prime number q and prime power	given a prime number q and prime power q with positive integers m and d such that d ≤ q − 1, a primitive narrow-sense bch code over the finite field (or galois field) gf(q) with code length n = q − 1 and distance at least d is constructed by the following method.	wikipedia
ddec727f6b6280086331d697c5698d6661cddf1b	one of the key features of bch codes	one of the key features of bch codes is that during code design, there is a precise control over the number of symbol errors correctable by the code. in particular, it is possible to design binary bch codes that can correct multiple bit errors. another advantage of bch codes is the ease with which they can be decoded, ...	wikipedia
6d6bf953ab3529b758aa02ef3520c24ac2123096	in coding theory, the bose – chaudhuri –	in coding theory, the bose – chaudhuri – hocquenghem codes (bch codes) form a class of cyclic error-correcting codes that are constructed using polynomials over a finite field (also called a galois field). bch codes were invented in 1959 by french mathematician alexis hocquenghem, and independently in 1960 by raj chand...	wikipedia
33d5d586a1ded3cdb1f109709cc1c28a9b871359	aspilia mossambicensis, also known as wild sunflower, is	aspilia mossambicensis, also known as wild sunflower, is a medicinally useful herbaceous plant of the family compositae (asteraceae). it is widespread with an anthropogenic distribution in central and eastern tropical africa from ethiopia, through east africa, the congo, zambia, zimbabwe, malawi, mozambique and south a...	wikipedia
217e767dfbc8302b87f76d009b5e03eea904cb32	two powerful stimulators of uterine contraction, the diterpenes	two powerful stimulators of uterine contraction, the diterpenes kaurenoic and grandiflorenic acids, were found in the leaves of aspilia mossambicensis. this lends credence to the idea that wild chimpanzees consume leaves of aspilia species because of their pharmacological properties and could shed light on female chimp...	wikipedia
77f69116bf888e0ed07f61734aa9329e826add42	a. mossambicensis is used by herbalists and local	a. mossambicensis is used by herbalists and local people to treat such ailments and conditions as malaria, bacterial infection and human immunodeficiency virus (hiv). it is also used to reduce menstrual cramps as well as a uterotonic able to induce uterine contraction and labour in confinements. this species is used to...	wikipedia
896abd531782ebca8d0bc687f46f3f96d5e9c00e	herb or shrub 0.5–1 m or straggling bush	herb or shrub 0.5–1 m or straggling bush to 2.5 m high; branches scabrid. leaves sessile to shortly petiolate, ovate or elliptic, 2–12´1–3 cm, base cuneate, margins entire or serrate, apex acute or attenuate, scabrid on both surfaces, somewhat 3‑nerved from base; petiole up to 1 cm long. capitula in loose paniculate co...	wikipedia
0dfada8c862acf6262ad786f974ffd12db875015	aspilia mossambicensis, also known as wild sunflower, is	aspilia mossambicensis, also known as wild sunflower, is a medicinally useful herbaceous plant of the family compositae (asteraceae). it is widespread with an anthropogenic distribution in central and eastern tropical africa from ethiopia, through east africa, the congo, zambia, zimbabwe, malawi, mozambique and south a...	wikipedia
c95cb6cdf6f7fc8eb5e45de32fde932022649902	on 29 june 2016, dabo signed a two-year	on 29 june 2016, dabo signed a two-year contract with azerbaijan premier league side gabala fk. on 17 june 2018, dabo signed a two-year contract with fellow azerbaijan premier league club neftçi pfk.	wikipedia
380b904c2e8b8098ccadd2e175a56bef23cb82cf	in the 2004 intel science talent search, more	in the 2004 intel science talent search, more children (18) have parents who entered the country on h-1b (professional) visas than parents born in the united states (16). new h-1b visa holders each year represent less than 0.04 percent of the u.s. population. foreign born faculty now account for over 50% of faculty in ...	wikipedia
7d2b6359c8745f7cd8e438dfee75c22e8e2c2cd0	among 1985 foreign-born engineering doctorate holders, about 40%	among 1985 foreign-born engineering doctorate holders, about 40% expected to work in the united states after graduating. an additional 17 percent planned to stay on as post-doctorates, and most of these are likely to remain permanently in the united states. thus, almost 60% of foreign-born engineering doctorate holders...	wikipedia
34edccbf9dcfa744e78634183707fa1c9249244f	in recent years, the number of applicants for	in recent years, the number of applicants for faculty openings at research universities have increased dramatically. numbers of 50 to 200 applications for a single faculty opening have become typical, yet even with such high numbers of applicants, the foreign-born component is in excess of 50%. 60% of the top science s...	wikipedia
d628f306cf3ed165e30ffb42db53cd20b72d9247	in 1982, foreign-born engineers constituted about 3.6% of	in 1982, foreign-born engineers constituted about 3.6% of all engineers employed in the united states, 13.9% of which were naturalized; and foreign-born phds in engineering constituted 15% and 20% were naturalized. in 1985, foreign-born phds represented almost 33% of the engineering post-doctorate researchers in us uni...	wikipedia
28925ecf9bfc739c984321ca8a64edda180ed4b9	at the undergraduate level, us-born engineering students constitute	at the undergraduate level, us-born engineering students constitute upwards of 90–95% of the student population (most foreign-born candidates for engineering graduate schools are trained in their home countries). however, the pool of bs engineering graduates with us citizenship is much larger than the number who apply ...	wikipedia
e1c0046f74962c75a98a5c851384d6decae84ac3	although the united states continues to attract the	although the united states continues to attract the largest number and fraction of foreign students worldwide, its share of foreign students has decreased in recent years. 55% of phd students in engineering in the united states are foreign-born (2004). between 1980 and 2000, the percentage of phd scientists and enginee...	wikipedia
eca3873bcbcdadbe0ecae9c7fcf706e9dcaf0b6c	significant numbers of foreign-born students in science and	significant numbers of foreign-born students in science and engineering are not unique to america, since foreign students now account for nearly 60% of graduate students in mathematics, computer sciences, and engineering globally. in switzerland and the united kingdom, more than 40% of doctoral students are foreign. a ...	wikipedia
36aa688d5f8eac574d62c40867b2975c96d04220	in the united states, a significant proportion of	in the united states, a significant proportion of scientists and engineers are foreign-born, as well as students in science and engineering programs. however, this is not unique to the us since foreigners make up significant amounts of scientists and engineers in other countries. as of 2011, 28% of graduate students in...	wikipedia
b69a5aba4c8653fbd41f7df8b75eb0d1f3928891	on ash wednesday, march 5, 2014, the presidents	on ash wednesday, march 5, 2014, the presidents of 28 catholic and jesuit colleges and universities joined the "fast for families" movement. the "fast for families" movement reignited the immigration debate in the autumn of 2013 when the movement's leaders, supported by many members of congress and the president, faste...	wikipedia
2de2aab1eff9911102171d5e3924f3a016f812b0	scientific laboratories and startup internet opportunities have been	scientific laboratories and startup internet opportunities have been a significant factor in immigration to the united states. by 2000, 23% of scientists with a phd in the u.s. were immigrants, including 40% of those in engineering and computers. roughly a third of the united states' college and universities graduate s...	wikipedia
bf4e1637a5e9ab5793910332f810f180c4bc5df4	some scholars focus on the organization of "crimmigration"	some scholars focus on the organization of "crimmigration" as it relates to the mass removal of certain immigrants. jennifer chacón finds that immigration law enforcement is being decentralized. customs and border patrol (cbp), immigration and customs enforcement (ice), and the department of homeland security (dhs) are...	wikipedia
79a149df62fb21bc554238b0cfeebb1364a3c1a9	"crimmigration" recognizes how laws and policies throughout different	"crimmigration" recognizes how laws and policies throughout different states contribute to the convergence of criminal law enforcement and immigration law. for example, states are implementing a variety of immigration-related criminal offenses that are punishable by imprisonment. california, oregon, and wyoming crimina...	wikipedia
2a202a9b5ef765a22f771fae3a5c385ef037f7b5	using a "crimmigration" point of thought, césar cuauhtémoc	using a "crimmigration" point of thought, césar cuauhtémoc garcía hernández explains the criminalization of undocumented immigrants began in the aftermath of the civil rights movement. michelle alexander explores how the u.s. criminal justice system is made of "colorblind" policies and law enforcement practices that ha...	wikipedia
ff897ce46983eebc79de0c9aa136b7b7f62324d9	crimmigration has emerged as a field in which	crimmigration has emerged as a field in which critical immigration scholars conceptualize the current immigration law enforcement system. crimmigration is broadly defined as the convergence of the criminal justice system and immigration enforcement, where immigration law enforcement has adopted the "criminal" law enfor...	wikipedia
c2d6ca6f1ef24b86d4c8f2d4e245c4c16d8a869a	research suggests that police practices, such as racial	research suggests that police practices, such as racial profiling, over-policing in areas populated by minorities and in-group bias may result in disproportionately high numbers of racial minorities among crime suspects. research also suggests that there may be possible discrimination by the judicial system, which cont...	wikipedia
d7bd5407f3f1a3c64c633e69da99008141002f30	for the early twentieth century, one study found	for the early twentieth century, one study found that immigrants had "quite similar" imprisonment rates for major crimes as natives in 1904 but lower for major crimes (except violent offenses; the rate was similar) in 1930. contemporary commissions used dubious data and interpreted it in questionable ways.	wikipedia
a92c013c6fba30fb1fe10c3f5290452ca151a134	one of the first political analyses in the	one of the first political analyses in the u.s. of the relationship between immigration and crime was performed in the beginning of the 20th century by the dillingham commission, which found a relationship especially for immigrants from non-northern european countries, resulting in the sweeping 1920s immigration reduct...	wikipedia
863c77f1a32c399ea49aa3149a5d54243662fa1a	a 2018 study found that undocumented immigration to	a 2018 study found that undocumented immigration to the united states did not increase violent crime. research finds that secure communities, an immigration enforcement program which led to a quarter of a million of detentions (when the study was published; november 2014), had no observable impact on the crime rate. a ...	wikipedia
971bde62613d0a42a69b58a3338043eebc36f51f	a 2005 study showed that immigration to large	a 2005 study showed that immigration to large u.s. metropolitan areas does not increase, and in some cases decreases, crime rates there. a 2009 study found that recent immigration was not associated with homicide in austin, texas. the low crime-rates of immigrants to the united states despite having lower levels of edu...	wikipedia
9fa42f52f5fd89c2d6c7167ed4c4fe18eec6c231	there is no empirical evidence that either legal	there is no empirical evidence that either legal or illegal immigration increases crime in the united states. in fact, a majority of studies in the u.s. have found lower crime rates among immigrants than among non-immigrants, and that higher concentrations of immigrants are associated with lower crime rates. explanatio...	wikipedia