Optimal binary linear codes from maximal arcs
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
Optimal binary linear codes from maximal arcs
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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 ... 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.
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 … 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 …
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 … 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 …
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 …
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. litmus building nottingham addressWebJan 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 … litmus building nottingham postcodeWebJan 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 … litmus base colorWebOct 6, 2024 · In this paper, two families of binary subfield codes with a few weights are presented from two special classes of linear codes, and their parameters are explicitly … litmus blue to redWebMay 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 … litmus building nottingham for salelitmus certifiedWebDec 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 … litmuschaos github