Two Classes of Constacyclic Codes With a Square-Root-Like Lower Bound

IF 2.2 3区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Information Theory Pub Date : 2024-09-23 DOI:10.1109/TIT.2024.3464630

Tingfang Chen;Zhonghua Sun;Conghui Xie;Hao Chen;Cunsheng Ding

引用次数: 0

Abstract

Constacyclic codes over finite fields are an important class of linear codes as they contain distance-optimal codes and linear codes with best known parameters. They are interesting in theory and practice, as they have the constacyclic structure. In this paper, an infinite class of q-ary negacyclic codes of length

$(q^{m}-1)/2$

and an infinite class of q-ary constacyclic codes of length

$(q^{m}-1)/(q-1)$

are constructed and analyzed. As a by-product, two infinite classes of ternary negacyclic self-dual codes with a square-root-like lower bound on their minimum distances are presented.

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具有类似方根下限的两类恒环码

有限域上的常簇码是一类重要的线性码，因为它们包含距离最优码和具有已知参数的线性码。由于它们具有常环结构，因此在理论和实践中都很有趣。本文构建并分析了长度为 $(q^{m}-1)/2$ 的无穷类 q-ary 负循环码和长度为 $(q^{m}-1)/(q-1)$ 的无穷类 q-ary 常循环码。作为副产品，还提出了两类无限的三元负环自偶码，它们的最小距离具有类似平方根的下限。

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

IEEE Transactions on Information Theory 工程技术-工程：电子与电气

CiteScore

5.70

自引率

20.00%

发文量

514

审稿时长

12 months

期刊介绍： The IEEE Transactions on Information Theory is a journal that publishes theoretical and experimental papers concerned with the transmission, processing, and utilization of information. The boundaries of acceptable subject matter are intentionally not sharply delimited. Rather, it is hoped that as the focus of research activity changes, a flexible policy will permit this Transactions to follow suit. Current appropriate topics are best reflected by recent Tables of Contents; they are summarized in the titles of editorial areas that appear on the inside front cover.