Optimal binary linear codes from maximal arcs
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 … 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....
Optimal binary linear codes from maximal arcs
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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 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, …
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 … 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 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 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.
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 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 ... inconsistency\\u0027s 5WebDec 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 … inconsistency\\u0027s 59WebOptimal 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. … inconsistency\\u0027s 5rWebAbstract 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. inconsistency\\u0027s 58inconsistency\\u0027s 5aWebJan 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 … inconsistency\\u0027s 61Webbinary 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 … inconsistency\\u0027s 5t