Optimal minimal linear codes from posets

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 … 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.

Minimal vectors in linear codes IEEE Journals & Magazine IEEE …

Web11 rows · Sep 11, 2024 · In this paper, we focus on constructions of distance-optimal binary (minimal) linear codes ... 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. grasim industries dahej industrial expo https://the-traf.com

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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 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 … 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 … grasim industries headquarters

Optimal minimal Linear codes from posets DeepAI

Category:Optimal minimal linear codes from posets SpringerLink

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Optimal minimal linear codes from posets

Maximum distance separable poset codes SpringerLink

WebDec 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 … WebSep 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 …

Optimal minimal linear codes from posets

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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 … WebA 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 …

WebMay 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 … 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 …

WebAbstract: Minimal vectors in linear codes arise in numerous applications, particularly, in constructing decoding algorithms and studying linear secret sharing schemes. However, … 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 …

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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 ... chitin cave ark the islandWebpresent 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 … grasim industries cementWebApr 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. chitin cave ark locationWebRecently, 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. grasim industries investor presentationWebJun 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. grasim industries hr headgrasim industries isin codeWebfamilies 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 ... chitin cave fjordur