On the minimum distance of cyclic codes

Author: etle

August undefined, 2024

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 … 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.

A Bound on the Minimum Distance of Quasi-cyclic Codes

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 … 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 … cumulative sum of array

arXiv:2105.15086v1 [cs.IT] 31 May 2024

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 … 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 … Web10 de abr. de 2010 · We show that the minimum distance of a linear code ... We also characterize the affine-invariant maximal extended cyclic codes. Then by the CSS … cumulative sum of latest 3 weeks

Generalizing Bounds on the Minimum Distance of Cyclic Codes …

A new bound on the minimum distance of cyclic codes …

Web2 de mai. de 2024 · 1 Answer Sorted by: 1 The question should be the minimum distance is at least 4. (NTU final exam,right?) Suppose f ( x) is a nonzero codeword in C with … 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 … cumulative sum of forecast errorsWebgive a new proof to a result of [3] which says that the minimum distance, d min, for PAC codes is greater than or equal to the d min for polar codes. The usage of cyclic shifts in our work is motivated by the work of [4], which designs and analyzes a particular permutation set of polar codes relying on a N=4-cyclic shift for practical ... easyantycheat如何下载

"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 all ternary cyclic codes of length less than 40 and having a minimum distance exceeding the BCH bound. It seems that almost all lower bounds are equal to the minimum distance. " - On the minimum distance of cyclic codes

On the minimum distance of cyclic codes

coding theory - Finding minimum distance of a cyclic code

WebIndex Terms—Cyclic Code, Cyclic Product Code, Bound on the Minimum Distance, Efﬁcient Decoding I. INTRODUCTION Cyclic codes play a central role in (distributed) … Web3 de mar. de 2024 · arXivLabs: experimental projects with community collaborators. arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Did you know?

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 … 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 …

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...

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

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 …

WebTheorem I: Let C, be a binary cyclic code of length n (odd) with generator gl(x), and let C, be a binary cyclic code of length n with generator g,(x)g,(x). Let di be the minimum distance of Ci, i = 1,2. Then the binary cyclic code C of length 2n with generator g:(x)g2(x) is equivalent to the IuIu + UI sum of C, and C,. cumulative sum using window functionWebcodes (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 … cumulative sum of array in javaWeb19 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 … cumulative sum of forecast errors formulaWebThe 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 … cumulative sum of salary in sqlWeb9 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 … easyantichent下载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. cumulative table powerbiWeb26 de jan. de 2013 · Generalizing Bounds on the Minimum Distance of Cyclic Codes Using Cyclic Product Codes Alexander Zeh, Antonia Wachter-Zeh, Maximilien … easy anti inflammatory lunch