Optimal binary linear codes from maximal arcs

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August undefined, 2024

WebThe 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 ... 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.

Infinite Families of Optimal Linear Codes Constructed From …

WebAbstract: A linear code is optimal if it has the highest minimum distance of any linear code with a given length and dimension. We construct infinite families of optimal binary linear codes C Δc constructed from simplicial complexes in F 2 n, where Δ is a simplicial complex in F 2 n and Δ c the complement of Δ. We first find an explicit computable criterion for C … 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... shuttle nippon express

A new class of optimal linear codes with flexible parameters

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 … 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 … 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 … shuttle night launch

Li Xu, Cuiling Fan, Sihem Mesnager, Rong Luo

[2001.01049] Optimal Binary Linear Codes from Maximal Arcs

WebMar 11, 2024 · The main purpose of this paper is to construct a class of linear codes over R by the approach mentioned above. By the Gray map, we can obtain a class of linear codes over F q and these linear codes are optimal with respect to the Griesmer bound. Notably, to our best knowledge, the parameters of these optimal linear codes are new. WebJan 4, 2024 · Using maximal arcs in PG(3, 2m), we give a new proof of the fact that the binary cyclic code C(m)1, 22h−2h+1, the code of length 2m−1 with defining zeroes α and … shuttle nice airport monacoWebThe 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 … shuttle notes clothing

"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

WebOptimal 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. … 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 ...

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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. 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 …

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 … 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 …

WebMay 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 … 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....

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 …

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 … the park arlington ridgeWebA 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 … shuttle notes シャツWebIn 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. the park apartments tucson azWebDec 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 … the park aquaWebThere 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 ... shuttle not readyWeblater 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]. the park aspenWebAn 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: … the park apartments tallahassee