On the minimum distance of cyclic codes

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 … Web1 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...

Minimum Distance of PAC Codes v. Polar Codes Using Cyclic …

Web7 de dez. de 1998 · It is desired to develop a method that can derive the weight distribution with high speed, or the minimum distance and the number of corresponding code words. Recently, Barg and Dumer [5] proposed a method in which the minimum distance and the number of corresponding code words are determined efficiently, by utilizing the … 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 ]). first time home buyer ira withdrawal https://gs9travelagent.com

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

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 Web7 de dez. de 1998 · It is desired to develop a method that can derive the weight distribution with high speed, or the minimum distance and the number of corresponding code … 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 … campground manager

Minimum Distance of PAC Codes v. Polar Codes Using Cyclic Shift …

Category:The minimum Hamming distances of irreducible cyclic codes

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On the minimum distance of cyclic codes

On the minimum distance of certain reversible cyclic codes …

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 · 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 …

On the minimum distance of cyclic codes

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WebKeywords: Finite elds, cyclic codes, trace representations, permutation polynomials. Abstract Estimation of the minimum distance of cyclic codes is a classical problem in … 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 …

WebIt 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 … 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; …

WebThe 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 … 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, …

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 …

first time home buyer in texasWebSince 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 … first time homebuyer iraWebIndex Terms—Cyclic Code, Cyclic Product Code, Bound on the Minimum Distance, Efficient Decoding I. INTRODUCTION Cyclic codes play a central role in (distributed) … campground manager jobs wisconsinWeb10 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 … campground manager jobs near meWeb1 de set. de 2014 · The minimum Hamming distances of irreducible cyclic codes September 2014 Finite Fields and Their Applications 29:225–242 DOI: 10.1016/j.ffa.2014.05.003 Authors: Fengwei Li Qin Yue Nanjing... campground manager jobs ontarioWebThis bound is related to a second method for bounding the minimum distance of a cyclic code, which we call shifting. This method can be even stronger than the first one. For all binary cyclic codes of length < 63 (with two exceptions), we show that our methods yield … campground manager salaryWebThe main result is a new lower bound for the minimum distance of cyclic codes that includes earlier bounds (i.e., BCH bound, HT bound, Roos bound). This bound is related to a second method for bounding the minimum distance of a cyclic code, which we call shifting. This method can be even stronger than the first one. For all binary cyclic codes … campground map designer