Some minimal cyclic codes over finite fields
WebFinite Fields and Their Applications. Volume 63, March 2024, 101633. Asymptotically good Z p r Z p s-additive cyclic codes WebA cyclic code has been one of the most active research topics in coding theory because they have many applications in data storage systems and communication systems. They have …
Some minimal cyclic codes over finite fields
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WebFlag codes that are orbits of a cyclic subgroup of the general linear group acting on flags of a vector space over a finite field, are called cyclic orbit flag codes. In this paper, we present a new contribution to the study of such codes, by focusing this time on the generating flag. More precisely, we examine those ones whose generating flag has at least one subfield … WebApr 26, 2024 · p ~ ( x) = x 6 + x 5 + 1 = x 6 p ( 1 x). From this we see immediately α − 1 and α − 2 are zeros of the factor p ~ ( x). So we have shown that α j is a zero of the generator …
WebJan 1, 2024 · $\begingroup$ It would be easier to give a helpful answer, if you explained what you know about cyclic codes and Reed-Solomon codes. $\endgroup$ – Jyrki … WebSOME RESULTS ON BCH CODES OF LENGTH q m+1 2 5 Example 1. Let q= 3, m= 5 and 0 ≤i≤121. ... C. Ding and S. Li,LCD cyclic codes over finite fieldsIEEE Trans. Inf. Theory, , 63 …
WebFinally, we give some examples of self-dual, isodual, MDS and quasi-twisted codes corresponding to two-dimensional $(\alpha,\beta )$-constacyclic codes. Skip to search form Skip to main content Skip to account menu Web20.1.12 Best Known Codes. Magma incorporates databases containing constructions of the best known linear codes over F q for q = 2,3,4,5,7,8,9.These databases contain codes of …
WebMar 14, 2011 · Abstract: In coding theory, self-dual codes and cyclic codes are important classes of codes which have been extensively studied. The main objects of study in this …
Webin some cases, such codes can be decoded faster than other linear codes using nearest neighbor decoding. In [6], necessary and sufficient conditions for cyclic codes to be … fn keys in windows 10WebApr 1, 2024 · Kai and Zhu [29] later proposed a method for generating quantum codes using cyclic codes of odd length over the finite chain ring F 4 + v F 4 with u 2 = 0. Further, Qian [18] has introduced a method for generating quantum error-correcting codes using cyclic codes over the finite non-chain ring F 2 + v F 2 with arbitrary length v 2 = v. fn keys in windows 11WebA cyclic code has been one of the most active research topics in coding theory because they have many applications in data storage systems and communication systems. They have … greenway chambers youtubeWebJan 2024 - Mar 20241 year 3 months. San Francisco Bay Area. - Tech Lead on SDV reaction time and system latency. - Work on autonomy system challenges in self driving vehicles. - … fn keys offWebA Sequence Construction of Cyclic Codes over Finite Fields 3 2.1 Some notation and symbols fixed throughout this paper Throughout this paper, we adopt the following … fn keys settings windowsWebMay 26, 2024 · Finally we construct a linear MSRD code over an arbitrary finite field ... \ldots, t-1$, for any given minimum sum-rank distance. There is no restriction on the block ... A sum-rank-metric code attaining the Singleton bound is constructed over some F q -linear MSRD code over some field F q with different matrix sizes n 1 > n 2 ... fn keys excelWeblocal ring；cyclic codes；repeated-root codes；the number of codewords. 2010 MR Subject Classification：94B05；94B15. Document code：AArticle ID：0255-7797（2016）05 … fn keys shortcuts