Optimal minimal linear codes from posets
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 … 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.
Optimal minimal linear codes from posets
Did you know?
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...
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 ... 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 …
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. 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 …
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 …
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 … dhp south ayrshire councilWebMar 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 ... cinch peugeotWeb11 rows · Sep 11, 2024 · In this paper, we focus on constructions of distance-optimal binary (minimal) linear codes ... cinch parkWebThe 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]. dhp south cambsWebRecently, 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 … cinch peugeot 108WebRecently, 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. dhp southernWebAbstract: Minimal vectors in linear codes arise in numerous applications, particularly, in constructing decoding algorithms and studying linear secret sharing schemes. However, … cinch player of the season