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} … 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 …
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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 ... 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. …
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 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...
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. 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.
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 …
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 … chivalry unlock helmetsWebThe 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 … chivalry updateWebThere 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 ... grasshoppers mating ritualWebMay 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 … chivalry urban dictionaryWeblater 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]. chivalry verbWebMar 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. grasshoppers meaningWebJan 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 … grasshoppers memory deluxe