On the minimum distance of cyclic codes

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August undefined, 2024

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,. 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 …

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 … 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 … red fila sweatpants

On the minimum distance of cyclic codes - IEEE Xplore

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 … 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 … 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 … knockout js chrome extension

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

[PDF] Minimum Distance of PAC Codes v. Polar Codes Using Cyclic …

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 … 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 $q$. knockout in a sentenceWeb7 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 … red fila shorts

"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. " - On the minimum distance of cyclic codes

On the minimum distance of cyclic codes

[PDF] Minimum Distance of PAC Codes v. Polar Codes Using Cyclic …

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... 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 …

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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 … 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.

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, … 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 weight at most 3, say f = a x i + b x j + c x k, where 0 ≤ i < j < k < n . Since g ( x) f ( x), then f ( α) = f ( α 2) = f ( α 3) = 0, so a α i l + b α j l + c α k l = 0, l = 1, 2, 3.

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 … WebThe minimum distance of a class of reversible cyclic codes has been proved to be greater than that given by the BCH bound.

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 …

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 … knockout hydraulic punch greenleeWeb15 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 … knockout js dynamic html bindingWeb3 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. knockout js hasfocusWeb10 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 … red fila shoes mensWeb8 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 ... red fila shoes womensWebFinally, we provide an upper bound on the minimum distance for nonbinary quasi-cyclic LDPC codes. areas of communications and signal processing, ... Lei Liu, Jie Huang, Wuyang Zhou, Shengli Zhou. "Computing the Minimum Distance of Nonbinary LDPC Codes." IEEE Transactions on Communications 60.7 (2012) 1753-1758 MLA; Harvard; … knockout js html bindingWebA 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 … red fila sneakers