Optimal binary linear codes from maximal arcs

Author: ggsa

August undefined, 2024

WebThe second objective is to construct a class of distance-optimal binary codes with parameters [{2^{m}+2, 2^{m}-2m, 6}]. Both classes of binary linear codes have new … WebAn 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: …

Optimal Subcodes of Second Order Reed-Muller Codes andMaximal Linear …

WebMay 8, 2009 · 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 time our results sharply limit the … 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… portland oregon photography clubs

Optimal Binary Linear Codes from Maximal Arcs - HKUST SPD

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 … 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. 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 … optimize start menu cache files task manager

On the maximality of linear codes SpringerLink

Optimal Binary Linear Codes From Maximal Arcs

WebJan 30, 2024 · Optimal 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 class of binary linear codes with parameters ... Webbinary linear codes with parameters [2m+ s+2 −2m,2m+s+2 −2m−2m−2,4], which have better information rates than the class of extended binary Hamming codes, and are also … optimize software for windows 10Weba class of binary linear codes with parameters [2m+s+2s−2m,2m+s+2s−2m−2m−2,4]superscript2𝑚𝑠superscript2𝑠superscript2𝑚superscript2𝑚𝑠superscript2𝑠superscript2𝑚2𝑚24[2^{m+s}+2^{s} … portland oregon phone directory residential

"WebThere are exactly two non-equivalent [32,11,12] -codes in the binary Reed-Muller code {\\cal{RM}}(2,5) which contain {\\cal{RM}}(1,5) and have the weight set \\{0,12 ... " - Optimal binary linear codes from maximal arcs

Optimal binary linear codes from maximal arcs

WebMar 20, 2024 · In this paper we consider binary linear codes spanned by incidence matrices of Steiner 2-designs associated with maximal arcs in projective planes of even order, and their dual codes.... 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 …

Did you know?

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] 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 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 … Weblater extended in [49], [51]. In [24], optimal binary linear codes were constructed from maximal arcs. Meanwhile, in [26], they presented the subﬁeld codes of [q+1,2,q] MDS codes with different forms of generator matrix and some optimal linear codes are obtained. The subﬁeld codes of some cyclic codes were also studied in [25], [47].

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 … WebOptimal 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 …

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 …

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 … optimize social security benefits calculatorWebThe 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 … portland oregon pgeWebAug 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. optimize specific high-capacity hddWeblinear 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 … portland oregon permitsWebOptimal 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. … optimize soundWebIn this paper, let $ q $ be a power of a prime, we construct several classes of new projective three-weight or four-weight linear codes over $ \mathbb{F}_q $ from the defining sets construction, and determine their weight distributions by using additive character sums. Especially, these codes are suitable for applications in secret sharing schemes. optimize teams for vdiWebJan 30, 2024 · In [24], optimal binary linear codes were constructed from maximal arcs. Meanwhile, in [26], they presented the subfield codes of [q + 1, 2, q] MDS codes with … portland oregon physicians