Optimal binary linear codes from maximal arcs

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WebJan 4, 2024 · The optimality of these four families of linear codes are characterized with an explicit computable criterion using the Griesmer bound and several classes of (distance … WebThe binary Hamming codes with parameters $[2^m-1, 2^m-1-m, 3]$ are perfect. Their extended codes have parameters $[2^m, 2^m-1-m, 4]$ and are distance-optimal. The first objective of this paper is to construct a class of binary linear codes with parameters $[2^{m+s}+2^s-2^m,2^{m+s}+2^s-2^m-2m-2,4]$, which have better information rates than …

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WebA ℤ4-linear code of high minimum Lee distance derived from a hyperoval (with Johannes Zwanzger) Advances in Mathematics of Communications 5, 2 (2011-5, special issue ALCOMA'10), 275–286. Digital Object Identifier: 10.3934/amc.2011.5.275 Mathematical Reviews: MR2801593(reviewed by Giorgio Faina) Zentralblatt Math: 1252.94120 ERef … WebJan 4, 2024 · The optimality of these four families of linear codes are characterized with an explicit computable criterion using the Griesmer bound and several classes of (distance-)optimal linear codes with few weights are obtained, which are useful in applications. 1 PDF View 1 excerpt, cites background porbeagleshark replacement band

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WebJan 4, 2024 · Then the maximal arc code C(A) has parameters [n,3,n−h] and weight enumerator. 1+(q2−1)nhzn−h+(q3−1)h−(q2−1)nhzn, where n=hq+h−q. The dual C(A)⊥ has … WebOct 6, 2024 · In this paper, two families of binary subfield codes with a few weights are presented from two special classes of linear codes, and their parameters are explicitly … sharon s fancy dress

A class of subfield codes of linear codes and their duals ...

[2001.01049] Optimal Binary Linear Codes from Maximal …

WebThe newly obtained codewords each have length n−(d−1)=n−d+1,{\displaystyle n-(d-1)=n-d+1,} and thus, there can be at most qn−d+1{\displaystyle q^{n-d+1}}of them. Since C{\displaystyle C}was arbitrary, this bound must hold for the largest possible code with these parameters, thus:[2] WebAug 1, 2010 · Several new upper bounds on the maximum size of an optimal constant weight code are obtained, leading among other things to the exact values of 12,4,5)=80, and 15,6,6)=70. A binary code C ⊆ F 2 n with minimum distance at least d and codewords of Hamming weight w is called an (n , d , w >) constant weight code. por-bazhyn island fortressWebJan 1, 2024 · Subfield codes of linear codes over finite fields have recently received a lot of attention, as some of these codes are optimal and have applications in secrete sharing, … porbeagle nemesis hungry shark

"WebThe binary Hamming codes with parameters $[2^m-1, 2^m-1-m, 3]$ are perfect. Their extended codes have parameters $[2^m, 2^m-1-m, 4]$ and are distance-optimal. The first … " - Optimal binary linear codes from maximal arcs

Optimal binary linear codes from maximal arcs

Weblinear codes are the binary Hamming codes with parameters [2m−1,2m−1−m,3]. The extended binary Hamming codes have parameters [2m,2m−1−m,4] and are distance … WebJan 14, 2024 · The parameters of these binary linear codes are new in most cases. Some of the codes and their duals obtained are optimal or almost optimal. View Show abstract Binary LCD Codes and...

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WebJan 1, 2024 · Recently, subfield codes of some optimal linear codes have been studied. In this paper, we further investigate a class of subfield codes and generalize the results of … WebDec 15, 2024 · In this paper we firstly show that a binary code reaches one of the above bounds for δ_r () if and only if reaches the corresponding bounds for d_H and r is …

Weba class of binary linear codes with parameters [2m+s+2s−2m,2m+s+2s−2m−2m−2,4]superscript2𝑚𝑠superscript2𝑠superscript2𝑚superscript2𝑚𝑠superscript2𝑠superscript2𝑚2𝑚24[2^{m+s}+2^{s} … WebJan 29, 2024 · Optimal Binary Linear Codes From Maximal Arcs. The binary Hamming codes with parameters $[{2^{m}-1, 2^{m}-1-m, 3}]$ are perfect. Their extended codes have …

WebApr 7, 2024 · 算法(Python版）今天准备开始学习一个热门项目：The Algorithms - Python。参与贡献者众多，非常热门，是获得156K星的神级项目。项目地址 git地址项目概况说明Python中实现的所有算法-用于教育实施仅用于学习目… WebAbstract We study [2m-1,2m]-binary linear codes whose weights lie between w0 and 2m-w0, where w0 takes the highest possible value. Primitive cyclic codes with two zeros whose dual satisfies this property actually correspond to almost bent power functions and to pairs of maximum-length sequences with preferred crosscorrelation.

WebJan 4, 2024 · Title:Optimal Binary Linear Codes from Maximal Arcs. Authors:Ziling Heng, Cunsheng Ding, Weiqiong Wang. Download PDF. Abstract:The binary Hamming codes …

WebJan 30, 2024 · Abstract: The binary Hamming codes with parameters [2 m-1, 2 m-1- m, 3] are perfect. Their extended codes have parameters [2 m , 2 m - 1 - m, 4] and are distance … porbin offersWebMay 8, 2009 · We show that if a linear code admits an extension, then it necessarily admits a linear extension. There are many linear codes that are known to admit no linear extensions. Our result implies that these codes are in fact maximal. We are able to characterize maximal linear (n, k, d) q -codes as complete (weighted) (n, n − d)-arcs in PG(k − 1, q). At the same … sharon shafran facebook profilesWebOptimal Binary Linear Codes from Maximal Arcs Ziling Heng, Cunsheng Ding, and Weiqiong Wang Abstract The binary Hamming codes with parameters [2 m−1,2 −1−m,3]are perfect. … porbeagle shark uk recordWebOptimal Binary Linear Codes From Maximal Arcs. Abstract: The binary Hamming codes with parameters [2 m -1, 2 m -1- m, 3] are perfect. Their extended codes have parameters [2 m , 2 m - 1 - m, 4] and are distance-optimal. The first objective of this paper is to construct a … sharons feetWebThe binary Hamming codes with parameters [{2^{m}-1, 2^{m}-1-m, 3}] are perfect. Their extended codes have parameters [{2^{m}, 2^{m}-1-m, 4}] and are distance-optimal. The first objective of this paper is to construct a class of binary linear codes with parameters [{2^{m+s}+2^{s}-2^{m},2^{m+s}+2^{s}-2^{m}-2m-2,4}] , which have better information rates … por besitoWebThe only nontrivial inﬁnite family of perfect binary linear codes are the binary Hamming codes with parameters [2m−1,2m−1−m,3]. The extended binary Hamming codes have parameters [2m,2m−1−m,4] and are distance-optimal. The motivation of this paper is to search for a class of binary linear codes which are better than the extended ... porbandar weather live forecastWebAn optimal code is a code that is length-optimal, or dimension-optimal, or distance-optimal, or meets a bound for linear codes. A ∗Correspondingauthor. XiaoqiangWangandDabinZhengarewiththeHubeiKeyLaboratoryofAppliedMathematics,FacultyofMath- ematicsandStatistics,HubeiUniversity,Wuhan430062, China(E-mail: … por berto mac intel