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 … 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 …
Did you know?
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 ... 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....
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 … WebJan 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 …
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 ... 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. …
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. 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 … bird house baffleWebThe 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 … daly\u0027s seafin oilWebA 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 … daly\u0027s seafin ship\u0027n shoreWebJan 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 birdhouse bakery edmontonWeblater 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]. daly\u0027s restaurant ottawaWebA few chapters deal with designs obtained from linear codes in other ways. Connections among ovals, hyperovals, maximal arcs, ovoids, linear codes and designs are also investigated. This book consists of both classical results on designs from linear codes and recent results yet published by others. daly\\u0027s seafin oilWebJan 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 … birdhouse bakery muthill