Conflict-Avoiding Codes of Prime Lengths and Cyclotomic Numbers

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

IEEE Transactions on Information Theory Pub Date : 2024-08-09 DOI:10.1109/TIT.2024.3439714

Liang-Chung Hsia;Hua-Chieh Li;Wei-Liang Sun

引用次数: 0

Abstract

The problem to construct optimal conflict-avoiding codes of even lengths and the Hamming weight 3 is completely settled. On the contrary, it is still open for odd lengths. It turns out that the prime lengths are the fundamental cases needed to be constructed. In the article, we study conflict-avoiding codes of prime lengths and give a connection with the so-called cyclotomic numbers. By having some nonzero cyclotomic numbers, a well-known algorithm for constructing optimal conflict-avoiding codes will work for certain prime lengths. As a consequence, we are able to answer the size of optimal conflict-avoiding code for a new class of prime lengths.

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质数长度和循环数的避免冲突代码

构建偶数长度、汉明权重为 3 的最佳避免冲突编码的问题已经完全解决。相反，奇数长度的问题仍未解决。事实证明，质数长度是需要构建的基本情况。在这篇文章中，我们研究了质数长度的避免冲突编码，并给出了与所谓的回旋数之间的联系。通过一些非零的循环数，一种著名的构建最优避免冲突编码的算法将适用于某些素数长度。因此，我们能够回答一类新质数长度的最优冲突避免代码的大小。

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.