On the minimum distance of cyclic codes

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August undefined, 2024

WebSince 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 … Web4 de abr. de 2024 · By using the cyclic shift matrices, this study provides new proof that, from the minimum distance viewpoint, PAC codes are superior to polar codes. The polarization-adjusted convolutional (PAC) codes are a new family of linear codes that can perform close to the theoretical bounds. These codes make use of both polar coding and …

Computing the Minimum Distance of Nonbinary LDPC Codes

Web6 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. WebThe 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 … highland woods homeowners association

Use of Grobner bases to decode binary cyclic codes up to the true ...

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 … Web1 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... 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 … highland woods golf il

On computing the number of code words with minimum weight for cyclic ...

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; … Web12 de jul. de 2013 · Generalizing bounds on the minimum distance of cyclic codes using cyclic product codes Abstract: Two generalizations of the Hartmann-Tzeng (HT) bound … how is organic vinegar madeWeb10 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 … highland woods rv resort florida

"WebWe 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 … " - On the minimum distance of cyclic codes

On the minimum distance of cyclic codes

(PDF) On Binary Cyclic Codes with d=3 - ResearchGate

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 … Web9 de ago. de 2024 · A cyclic code is a cyclic q-ary code of length n, constant weight w and minimum distance d.Let denote the largest possible size of a cyclic code. The pure and mixed difference method plays an important role in the determination of upper bound on .By analyzing the distribution of odd mixed and pure differences, an improved upper bound …

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Webcodes (0,) of dimension k, in F,G, and cyclic codes d, in the rclatcd fields F,, s E I. Then d = C3, E, (0,) 0 24, is a 2-D cyclic code of dimension E, E ,k;dim(M,j. We can easily derive a … WebSeveral new classes of optimal ternary cyclic codes with minimum distance four. 1. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China. 2. Wuhan Maritime Communication Research Institute, Wuhan 430079, China. Let C ( u, v) denote the ternary cyclic code with two zeros αu …

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... 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 …

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 ...

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 ]).

Web6.1.2 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 … how is organism related to populationWebWe 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 $q$. highland woods health the woodlands txWeb7 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 … how is organizational culture usually formedWeb1 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. how is organizational culture definedWebdistance 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 … highland woods mobile home parkWeb9 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. how is organizational culture createdWebThe minimum distance of a class of reversible cyclic codes has been proved to be greater than that given by the BCH bound. highlandwoodworking.com free shipping