On the minimum distance of cyclic codes

Web20 de jul. de 1996 · The BCH code of length 1023 and designed distance 253 has minimum distance 253. The cyclic codes of length 2 11 Gamma 1; 2 13 Gamma 1; 2 17 Gamma 1, with generator polynomial m 1 (x) and m 7 (x ... Web15 de mar. de 2024 · In this paper, we provide two complementary results for cyclic codes of composite length. First, we give a general construction of cyclic codes of length nr …

On the minimum distance of cyclic codes - IEEE Xplore

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 Web2 de mai. de 2024 · 2. My goal is to find a generator polynomial for a binary [ 15, 5, d] cyclic code that corrects all errors with weight less than or equal to 3. I have to find a degree 10 monic polynomial that divides x 15 − 1 ( mod 2) and has weight 7. If 15 and 5 were coprime I would know how to factor x 15 − 1 using cyclotomic theory. tryphoera sunnyvale ca https://foxhillbaby.com

Optimal cyclic quaternary constant‐weight codes of weight three

Web30 de jun. de 2014 · And we also calculate the minimum distance of some cyclic codes and give lower bounds on the minimum distance for some other cyclic codes. Keywords: Cyclic codes, Whiteman generalized cyclotomic sequences, generator polynomial, minimum distance. Mathematics Subject Classification: Primary: 58F15, 58F17; … WebAbstract: The minimum distance of a class of reversible cyclic codes has been proved to be greater than that given by the BCH bound. It is also noted that this class of codes … Web10 de mai. de 2011 · 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 … phillip island nature park austrália

(PDF) Skew cyclic Linear codes over 𝑹 = 𝑅 + 𝑤𝑅 + 𝑤2𝑅

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On the minimum distance of cyclic codes

On the minimum distance of certain reversible cyclic codes (Corresp ...

Web9 de jun. de 2015 · Decoding of Repeated-Root Cyclic Codes up to New Bounds on Their Minimum Distance Alexander Zeh, Markus Ulmschneider The well-known approach of Bose, Ray-Chaudhuri and Hocquenghem and its generalization by Hartmann and Tzeng are lower bounds on the minimum distance of simple-root cyclic codes. Web1 de mar. de 1993 · On the minimum distance of ternary cyclic codes M. Eupen, J. H. Lint Published 1 March 1993 Computer Science IEEE Trans. Inf. Theory There are many ways to find lower bounds for the minimum distance of a cyclic code, based on investigation of the defining set. Some new theorems are derived.

On the minimum distance of cyclic codes

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WebWe give a general lower bound for the minimum distance of $q$-ary quasi-cyclic codes of length $m\ell$ and index $\ell$, where $m$ is relatively prime to $q$.

WebThe minimum distance of a class of reversible cyclic codes has been proved to be greater than that given by the BCH bound. 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 …

WebFinally, we provide an upper bound on the minimum distance for nonbinary quasi-cyclic LDPC codes. areas of communications and signal processing, ... Lei Liu, Jie Huang, Wuyang Zhou, Shengli Zhou. "Computing the Minimum Distance of Nonbinary LDPC Codes." IEEE Transactions on Communications 60.7 (2012) 1753-1758 MLA; Harvard; … 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 …

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 …

Web13 de mar. de 2014 · In coding theory estimating the minimum distance of a given code is one of the main problems, which has been studied by many researchers. Several bounds on the minimum distance are presented (such as Bose and Chaudhuri [ 1 ]; Hocquenghem [ 8 ]; Boston [ 3 ]; Hartmann and Tzeng [ 6 ]; Hartmann et al. [ 7 ]; Roos [ 9, 10 ]). try phoeraWebA 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 … phillip island near norfolk islandWebWe deal with the minimum distances of q -ary cyclic codes of length q m - 1 generated by products of two distinct minimal polynomials, give a necessary and sufficient condition for … phillip island news todayWeb6.1.2 Cyclic Codes. The most commonly used class of linear block codes is the cyclic codes. Examples of cyclic codes ... (011110), (100110), (101101), (110011), and (111000). Determine the minimum weights and the minimum distance of the code. Solution. As reflected in the following table, the minimum Hamming weight for this linear … try philo tvWeb1 de jan. de 2024 · Middle East Technical University Abstract Two bounds on the minimum distance of cyclic codes are proposed. The first one generalizes the Roos bound by embedding the given cyclic code into a... phillip island museumWeb14 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 … phillip island netballWeb19 de mar. de 2013 · Bounds on the Minimum Distance of Punctured Quasi-Cyclic LDPC Codes Abstract: Recent work by Divsalar has shown that properly designed protograph … phillip island nature resort villas