Optimal binary linear codes from maximal arcs
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 … 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} …
Optimal binary linear codes from maximal arcs
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WebMar 16, 2024 · The hull of a linear code C is the intersection of C with its dual. To the best of our knowledge, there are very few constructions of binary linear codes with the hull dimension $$\\ge 2$$ ≥ 2 except for self-orthogonal codes. We propose a building-up construction to obtain a plenty of binary $$[n+2, k+1]$$ [ n + 2 , k + 1 ] codes with hull … WebA 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.
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 · 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 …
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 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, …
chimera hoursWebOptimal 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 … chimera hobby shop black fridayWebJan 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... chimera home pageWebDec 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 … grados rankine a fahrenheit formulaWebIn 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. grado sr125x headphonesWebbinary 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 … chimerainvestment.comWebThere 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 ... chimera hologram