Optimal minimal linear codes from posets

WebApr 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.

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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 … 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. how to share access database with other users https://tipografiaeconomica.net

Optimal minimal linear codes from posets Designs, Codes and …

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 ... WebAug 17, 2024 · 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 … 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. how to share access to gmail account

Few-weight quaternary codes via simplicial complexes - AIMS …

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Optimal minimal linear codes from posets

Self-Orthogonal Codes Constructed from Posets and Their …

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 ... 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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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 … WebUpload an image to customize your repository’s social media preview. Images should be at least 640×320px (1280×640px for best display).

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.

WebRecently, some infinite families of optimal binary linear codes are constructed from simplicial complexes. Afterwards, the construction method was extended to using … 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 …

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

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 … how to share access on onedriveWebIn 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 … how to share access fileWebOPTIMAL MINIMAL LINEAR CODES FROM POSETS JONG YOON HYUN, HYUN KWANG KIM, YANSHENG WU, AND QIN YUE Abstract. Recently, some infinite families of minimal and … notify rfs of pile burnWebThe 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]. how to share access to ring cameraWebAug 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 … how to share access to google driveWebA 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 … notify revenue canada of a deathWebRecently, 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 … notify reporting