Optimal minimal linear codes from posets

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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 … 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 …

Optimal minimal Linear codes from posets - NASA/ADS

WebRecently, some infinite families of optimal binary linear codes are constructed from simplicial complexes. Afterwards, the construction method was extended to using … WebUpload an image to customize your repository’s social media preview. Images should be at least 640×320px (1280×640px for best display). irie kitchen bournemouth

Optimal minimal Linear codes from posets - arxiv-vanity.com

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. 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 … pool tuff products

New quaternary codes derived from posets of the disjoint …

Linear Codes from Simplicial Complexes over $\mathbb{F}_{2^n}$

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]. 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 ... irie jerk spanish townWebfamilies 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 ... irie love good love lyrics

"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. " - Optimal minimal linear codes from posets

Optimal minimal linear codes from posets

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 … 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.

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

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... 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 …

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.

Web11 rows · Sep 11, 2024 · In this paper, we focus on constructions of distance-optimal binary (minimal) linear codes ... pool tricksWebApr 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. irie mystic jamaican kitchen clarksville tnWebDec 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 … irie kitchen clevelandWebRecently, 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 … irie nation charlotteWebAug 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 … pool water balance calculatorWebMar 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 ... poolofficestopWebbinary 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 irie pc office