Optimal binary linear codes from maximal arcs

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August undefined, 2024

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 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 than … 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 …

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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 … 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} … invulnerability psychology definition

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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 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 … 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 … invulnerability mental health

1 Optimal Binary Linear Codes from Maximal Arcs

Two families of subfield codes with a few weights

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, … 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 ... invulnerability potion wowWebIn 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. invulnerability potion 5e

"WebThe 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 … " - Optimal binary linear codes from maximal arcs

Optimal binary linear codes from maximal arcs

Somepuncturedcodesofseveralfamiliesofbinarylinearcodes

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 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 …

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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. 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 ...

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 ... 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.

Weblinear 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 … WebJan 4, 2024 · Title:Optimal Binary Linear Codes from Maximal Arcs. Authors:Ziling Heng, Cunsheng Ding, Weiqiong Wang. Download PDF. Abstract:The binary Hamming codes …

Weblater 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].

WebDec 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 … invulnerability timeWebThe 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] invulnerability theory armyWebThe 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 … invulnerability windowsWebJan 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 invulnerability theory tenetsWebMar 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 … invulnera billboard weaknessWebAbstract 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. invulnerable artinyaWebJan 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 … invulnerability wikia