Optimal binary linear codes from maximal arcs
WebThe newly obtained codewords each have length n−(d−1)=n−d+1,{\displaystyle n-(d-1)=n-d+1,} and thus, there can be at most qn−d+1{\displaystyle q^{n-d+1}}of them. Since C{\displaystyle C}was arbitrary, this bound must hold for the largest possible code with these parameters, thus:[2] 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 …
Optimal binary linear codes from maximal arcs
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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 … 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 …
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 … 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.
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 … 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 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 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 … songs of war tygrenWebOct 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 … songs of war vinesWebJan 4, 2024 · Using maximal arcs in PG(3, 2m), we give a new proof of the fact that the binary cyclic code C(m)1, 22h−2h+1, the code of length 2m−1 with defining zeroes α and … small frame size of wide screen vodeoWebAbstract 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. small frame womens bicycleWebThere 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 ... small frames in bulkWebJan 4, 2024 · Title:Optimal Binary Linear Codes from Maximal Arcs. Authors:Ziling Heng, Cunsheng Ding, Weiqiong Wang. Download PDF. Abstract:The binary Hamming codes … songs of white lionWeblinear 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 … small frame spectacles uk