On the minimum distance of cyclic codes

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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 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 …

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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 … 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 … literally great sage crossword

The minimum Hamming distances of irreducible cyclic codes

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 … 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 … Web26 de abr. de 2024 · We can thus conclude that the minimum distance of this code is d m i n = 6. It may be worth observing that because x + 1 is a factor of the generator, all the … importance of good posture in communication

On the Construction of Quantum and LCD Codes from Cyclic Codes …

Cyclic codes from two-prime generalized cyclotomic sequences of order 6

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 … 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 … literally gorgeousWeb13 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 ]). importance of good listening

"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 … " - On the minimum distance of cyclic codes

On the minimum distance of cyclic codes

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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 … 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 …

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WebIndex Terms—Cyclic Code, Cyclic Product Code, Bound on the Minimum Distance, Efﬁcient Decoding I. INTRODUCTION Cyclic codes play a central role in (distributed) … 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 …

Web26 de jan. de 2013 · Generalizing Bounds on the Minimum Distance of Cyclic Codes Using Cyclic Product Codes Alexander Zeh, Antonia Wachter-Zeh, Maximilien … Webgive 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 ...

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 … 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 …

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; …

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 < 63 (with two exceptions), we show that our methods yield … literally great soulWebWe 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 $q$. importance of good roadsWebSince 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 … literally gospel meansWeb7 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 … importance of good presentation skillsWebThe 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 … literally got pantry staplesWeb15 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 … literally great soul crosswordWebWe 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 … literally guilty mind