pltkin -最优线性码的存在性

IF 2.9 3区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Information Theory Pub Date : 2025-06-25 DOI:10.1109/TIT.2025.3582936

Hopein Christofen Tang

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引用次数: 0

摘要

我们将$\mathbb {Z}_{4}$上线性码的Plotkin-type Lee距离界推广到几个新的更强的界。我们应用这些界来确定所有可能的整数n，使得对于任意给定的非负整数$k_{1}$和$k_{2}$，长度为n且类型为$4^{k_{1}}2^{k_{2}}$的$\mathbb {Z}_{4}$上存在普罗金最优线性码。我们进一步提供了$\mathbb {Z}_{4}$上每个可能长度的plotkin最优线性码的构造方法。我们的结果在很大程度上是通过考虑生成矩阵的列多重性来建立的。

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The Existence of Plotkin-Optimal Linear Codes Over ℤ4

We generalize the Plotkin-type Lee distance bound for linear codes over

$\mathbb {Z}_{4}$

to several new and stronger bounds. We apply these bounds to determine all possible integers n such that Plotkin-optimal linear codes over

$\mathbb {Z}_{4}$

of length n and type

$4^{k_{1}}2^{k_{2}}$

exist for any given non-negative integers

$k_{1}$

and

$k_{2}$

. We furthermore provide construction methods for Plotkin-optimal linear codes over

$\mathbb {Z}_{4}$

for each possible length mentioned above. Our results are in large part established by considering column multiplicities of generator matrices.

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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.