On the minimum distance of cyclic 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 … 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 $q$.

Decoding Cyclic Codes up to a New Bound on the Minimum …

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 … 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 ... eagle scout rank application pdf filler https://arcadiae-p.com

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

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 … 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 … 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 ]). csm bohannon

Bounds on the Minimum Distance of Punctured Quasi-Cyclic LDPC …

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On the minimum distance of cyclic codes

Decoding Cyclic Codes up to a New Bound on the Minimum Distance

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 … 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 …

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 ... WebThis 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 &lt; 63 (with two exceptions), we show that our methods yield …

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 … 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 …

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 … 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 …

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 …

WebIndex Terms—Cyclic Code, Cyclic Product Code, Bound on the Minimum Distance, Efficient Decoding I. INTRODUCTION Cyclic codes play a central role in (distributed) … csm body pillowWebPure - Aanmelden eagle scout rank application instructionsWeb1 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. eagle scout rank pictureWeb1 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... eagle scout rank application form 2022Web12 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 … csm bookshopWeb7 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 … csm boot biosWebgive 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 … csm bonus