大尺寸液晶编码的最小权重特征

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

IEEE Transactions on Information Theory Pub Date : 2024-10-18 DOI:10.1109/TIT.2024.3483218

Makoto Araya;Masaaki Harada;Keita Ishizuka;Yuto Tanaka

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引用次数: 0

摘要

我们给出了大维度液晶编码中最大最小权重的新特征。利用这些特征，我们完全确定了长度为 n、维数为 $n-6$ 的二元液晶编码，长度为 n、维数为 $n-5$ 的三元液晶编码，以及长度为 n、维数为 $n-4$ 的四元赫米特液晶编码中任意 n 的最大最小权重。

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Characterizations of the Minimum Weights of LCD Codes of Large Dimensions

We give new characterizations of the largest minimum weights among LCD codes of large dimensions. Using the characterizations, we completely determine the largest minimum weights among binary LCD codes of length n and dimension

$n-6$

, ternary LCD codes of length n and dimension

$n-5$

and quaternary Hermitian LCD codes of length n and dimension

$n-4$

for arbitrary n. We also determine the largest minimum weights among binary LCD codes of length n and dimension

$n-7$

, ternary LCD codes of length n and dimension

$n-6$

and quaternary Hermitian LCD codes of length n and dimension

$n-5$

with only some exceptions n.

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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.