Optimal binary linear codes from maximal arcs
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 … 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 …
Optimal binary linear codes from maximal arcs
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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 … 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 …
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 ... 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.
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 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]
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 …
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. … dailymotion im a celeb 2019WebJan 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 … dailymotion id x8omomWebThe 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 … dailymotion i love lucy s3ep31 subleaseWebJan 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, … biology chapter 3 test answersWebMar 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.... biology chapter 4 the energy of lifeWebMar 11, 2024 · The main purpose of this paper is to construct a class of linear codes over R by the approach mentioned above. By the Gray map, we can obtain a class of linear codes over F q and these linear codes are optimal with respect to the Griesmer bound. Notably, to our best knowledge, the parameters of these optimal linear codes are new. dailymotion i love lucyWebA 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. biology chapter 7 vocabulary