Two new constructions of cyclic subspace codes via Sidon spaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-24 DOI:10.1007/s10623-024-01466-y

Shuhui Yu, Lijun Ji

引用次数: 0

Abstract

A subspace of a finite field is called a Sidon space if the product of any two of its nonzero elements is unique up to a scalar multiplier from the base field. Sidon spaces, introduced by Roth et al. in (IEEE Trans Inf Theory 64(6):4412–4422, 2018), have a close connection with optimal full-length orbit codes. In this paper, we will construct several families of large cyclic subspace codes based on the two kinds of Sidon spaces. These new codes have more codewords than the previous constructions in the literature without reducing minimum distance. In particular, in the case of \(n=4k\), the size of our resulting code is within a factor of \(\frac{1}{2}+o_{k}(1)\) of the sphere-packing bound as k goes to infinity.

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通过西顿空间构建循环子空间编码的两种新方法

如果有限域的任意两个非零元素的乘积是唯一的，直到来自基域的标量乘数，那么这个有限域的子空间就叫做西顿空间。Roth 等人在（IEEE Trans Inf Theory 64(6):4412-4422, 2018）中提出的西顿空间与最优全长轨道编码有着密切联系。本文将在这两种西顿空间的基础上，构建几族大循环子空间码。与以往文献中的构造相比，这些新编码在不减少最小距离的情况下拥有更多的码字。特别是，在 \(n=4k\) 的情况下，当 k 变为无穷大时，我们所得到的编码的大小与球形打包约束的系数在 \(\frac{1}{2}+o_{k}(1)\) 之间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.