Optimal minimal linear codes from posets
WebThe Hamming weight wt(v) of v ∈ Fn2 is defined by the size of supp(v). We say that a linear code is distance-optimal if it has the highest minimum distance with prescribed length and dimension. An [n, k, d] linear code is called almost distance-optimal if the code [n, k, d + 1] is optimal, see [14, Chapter 2]. WebJul 19, 2024 · According to the latter Propositions 1 and 3, the code satisfying some conditions in Theorem 2 is distance optimal and minimal. 4 Proofs of the main results This section is divided into two parts. First, we give the statement of some lemmas. Next, we present the proofs of the main results.
Optimal minimal linear codes from posets
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WebMar 10, 2024 · Moreover, we present an infinite family of minimal quaternary linear codes, which also meet the Griesmer bound. ... Y. S. Wu, Q. Yue, Optimal minimal linear codes from posets, Des. Codes Cryptogr., 88 (2024), 2475-2492. doi: 10.1007/s10623-020-00793-0 [9] J. Y. Hyun, J. Lee, Y. Lee, Infinite families of optimal linear codes ... WebAug 17, 2024 · In this paper, we present two constructions of binary linear codes from hierarchical posets of two levels. In particular, we determine the weight distributions of …
WebJun 28, 2024 · Based on generic constructions of linear codes, Chang and Hyun constructed binary optimal and minimal linear codes via some simplicial complexes. The main idea of this letter is obtaining some binary optimal codes by employing posets of the disjoint union of two chains. Especially, anti-chains are corresponded to simplicial complexes. WebRecently, some infinite families of minimal and optimal binary linear codes were constructed from simplicial complexes by Hyun et al. We extend this construction method to arbitrary …
Webbinary optimal linear codes. Index Terms—Optimal codes, posets, weight distribution, Griesmer codes. I. INTRODUCTION L ET F 2be the finite field with two elements and let Fn be a vector space over F2. A linear code C of length n over F2 is a subspace of Fn 2 of dimension k. If C has minimal Hamming distance d, then C is called an [n,k,d]-code WebIn this paper, based on a generic construction of linear codes, we obtain four classes of optimal binary linear codes by using the posets of two chains. Two of them induce Griesmer codes which are not equivalent to the linear codes constructed by Belov. ... J. Y. Hyun, H. K. Kim, Y. Wu and Q. Yue, Optimal minimal linear codes from posets, Des ...
WebMar 1, 2024 · They constructed binary linear codes that are minimal as well as optimal, but the Ashikhmin-Barg condition (see [1]) does not hold for them. In [21], Zhu et al. studied codes over F 4 and...
WebRecently, some infinite families of minimal and optimal binary linear codes were constructed from simplicial complexes by Hyun et al. We extend this construction method to arbitrary posets. Especially, anti-chains are corresponded to simplicial complexes. how to watch barbarianWebpresent two constructions of binary linear codes from hierarchical posets of two levels. In particular, we determine the weight distributions of binary linear codes associated with … original gyro meatWebOPTIMAL MINIMAL LINEAR CODES FROM POSETS JONG YOON HYUN, HYUN KWANG KIM, YANSHENG WU, AND QIN YUE Abstract. Recently, some infinite families of minimal and … original gym badgeshow to watch barflyWebRecently, some infinite families of minimal and optimal binary linear codes were constructed from simplicial complexes by Hyun et al. We extend this construction method to arbitrary posets. Especially, anti-chains are corresponded to simplicial complexes. how to watch bare knuckle fcWebMay 31, 2024 · Abstract: Recently, some infinite families of minimal and optimal binary linear codes were constructed from simplicial complexes by Hyun {\em et al.} We extend … original haferlWebA result in LFSR sequences is used to illustrate the relation of the weights of codewords in two special codes obtained from simplical complexes and then determin the parameters of these codes. In this article we mainly study linear codes over $\mathbb{F}_{2^n}$ and their binary subfield codes. We construct linear codes over $\mathbb{F}_{2^n}$ whose defining … how to watch bare knuckle boxing