On the minimum distance of cyclic codes
Web1 de ago. de 2016 · Skew cyclic codes play the same role as cyclic codes in the theory of error-correcting codes for the rank metric. In this paper, we give descriptions of these … Web8 de jun. de 2009 · The Minimum Hamming Distance of Cyclic Codes of Length 2p s. June 2009. DOI: 10.1007/978-3-642-02181-7_10. Conference: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 18th ...
On the minimum distance of cyclic codes
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Web10 de abr. de 2024 · The primary goal of this article is to study the structural properties of cyclic codes over a finite ring R=Fq[u1,u2]/ u12−α2,u22 −β2 ... In view of Theorem 7, we conclude that there exists a quantum code [[120, 88, 3]] 5. which has the same minimum distance but a larger code rate than the best previously known ... Web14 de abr. de 2024 · PDF On Apr 14, 2024, Karima Chatouh published Skew cyclic Linear codes over 𝑹 = 𝑅 + 𝑤𝑅 + 𝑤2𝑅 ... Sum-rank BCH codes, with prescribed minimum sum-rank …
WebFor all binary cyclic codes of length < 63 (with two exceptions), we show that our methods yield the true minimum distance. The two exceptions at the end of our list are a code … Webdistance of ternary cyclic codes. Furthermore, the exact minimum distance of ternary cyclic codes of length less than 40 is computed numerically. A table is given containing …
WebSection 4 focuses on lower bounds for the minimum sum-rank distance of a cyclic-skew-cyclic code. We provide the analogues of the Roos bound and of the Hartmann-Tzeng bound, exploiting the notion of defining sets for cyclic-skew-cyclic codes. In Section 5 we focus on tensor products of codes. We combine a cyclic code in the Hamming Web30 de nov. de 2024 · Published: February 2024 The authors are supported by NTU Research Grant M4080456 Abstract Two bounds on the minimum distance of cyclic …
WebA general algebraic method for decoding all types of binary cyclic codes is presented. It is shown that such a method can correct t=[(d-1)/2] errors, where d is the true minimum distance of the given cyclic code. The key idea behind this decoding technique is a systematic application of the algorithmic procedures of Grobner bases to obtain the error …
WebSince every linear code is contained in an MDS linear code with the same minimum distance over some finite field extension, we focus our study on MDS linear codes. It is … pink thrasher hoodie buyWebIt turns out that lowest-code-rate cyclic codes with small minimum distances are useful for our approach. Therefore, we give a su cient condi-tion for binary cyclic codes of … pink three tier cartWebFlag 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 … pink three seater sofaWeb6 de jun. de 2009 · A note on negacyclic and cyclic codes of length p s over a finite field of characteristic p (2009) (submitted). Google Scholar Salagean, A.: Repeated-root cyclic and negacyclic codes over a finite chain ring. pink three piece suitWeb10 de mai. de 2011 · Decoding Cyclic Codes up to a New Bound on the Minimum Distance Alexander Zeh, Antonia Wachter, Sergey Bezzateev A new lower bound on the minimum distance of q-ary cyclic codes is proposed. This bound improves upon the Bose-Chaudhuri-Hocquenghem (BCH) bound and, for some codes, upon the Hartmann … pink three wheel strollerWebSince t is small, we conclude that our algorithm will have the running time discussed above if d ^ is large. This is the case for quadratic residue codes, since a quadratic residue code is essentially self-dual, and is also the case for most BCH codes since the minimal distance of their dual can be estimated via the Carlitz-Uchiyama bound [5] and other techniques … pink thrift shop logoWebThe bound involves the minimum distances of constituent codes of length ℓ as well as the minimum distances of certain cyclic codes of length m which are related to the fields … pink thrift obx