Optimal minimal linear codes from posets
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 were constructed from simplicial complexes by Hyun et al. We extend this construction …
Optimal minimal linear codes from posets
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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.
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. 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 …
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. 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 …
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].
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 … incoming rules firewallWebAug 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 … incoming scott adkinsWebJul 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. incoming schwedenWebMar 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... incoming scansWebA 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 … incoming seatac flightsWebUpload an image to customize your repository’s social media preview. Images should be at least 640×320px (1280×640px for best display). incoming scheduleWebRecently, 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 … incoming room