Optimal minimal linear codes from posets
WebMay 31, 2024 · Abstract: Recently, 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. WebOPTIMAL MINIMAL LINEAR CODES FROM POSETS JONG YOON HYUN, HYUN KWANG KIM, YANSHENG WU, AND QIN YUE Abstract. Recently, some infinite families of minimal and …
Optimal minimal linear codes from posets
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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. 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 ...
Webpresent 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 … 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.
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]. Webfamilies of binary optimal and minimal linear codes via simplicial complexes. Then Wu, Hyun, and Yue [9] extended the construction of linear codes to posets. Inspired by their work, we focus on the construction of quaternary codes via the posets of the disjoint union of two chains in this short letter. Let n be a positive integer and L be a ...
WebIn this paper, we present two constructions of binary linear codes from hierarchical posets of two levels. In particular, we determine the weight distributions of binary linear codes …
WebAug 17, 2024 · Recently, some infinite families of minimal and optimal binary linear codes are constructed from simplicial complexes by Hyun et al. We extend this construction … signs of blocked ureterWebSep 3, 2024 · (2) We present some optimal binary linear codes (Corollary 1), and we find some necessary and sufficient conditions for the binary linear codes constructed from … signs of blocked shuntsigns of blockage in colonWebA 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 … therapedic air mattressWebApr 12, 2008 · We derive the Singleton bound for poset codes and define the MDS poset codes as linear codes which attain the Singleton bound. In this paper, we study the basic properties of MDS poset codes. First, we introduce the concept of I -perfect codes and describe the MDS poset codes in terms of I -perfect codes. signs of blockage in intestinesWebDec 1, 2024 · Recently, some infinite families ofminimal and optimal binary linear codes were constructed from simplicial complexes by Hyun et al. We extend this construction … therapedic alder twin mattressWebMay 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 … signs of blood sugar crash