Two classes of optimal ternary cyclic codes with minimum distance four

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences Pub Date : 2023-01-01 DOI:10.1587/transfun.2023eal2055

Chao HE, Xiaoqiong RAN, Rong LUO

引用次数: 0

Abstract

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Let C(t,e) denote the cyclic code with two nonzero αt and αe, where α is a generator of 𝔽*3m. In this letter, we investigate the ternary cyclic codes with parameters [3m-1, 3m-1-2m, 4] based on some results proposed by Ding and Helleseth in 2013. Two new classes of optimal ternary cyclic codes C(t,e) are presented by choosing the proper t and e and determining the solutions of certain equations over 𝔽3m.

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最小距离为4的两类最优三元循环码

循环码是线性码的一个子类，由于具有高效的编码和解码算法，因此在消费电子、数据存储系统和通信系统中都有应用。设C(t,e)表示具有两个非零αt和αe的循环码，其中α是一个生成函数。本文基于Ding和Helleseth在2013年提出的一些结果，研究了参数为[3m- 1,3m -1-2m, 4]的三元循环码。通过选择合适的t和e，确定𝔽3m上若干方程的解，给出了两类新的最优三元循环码C(t,e)。

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

Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences 工程技术-工程：电子与电气

CiteScore

1.10

自引率

20.00%

发文量

137

审稿时长

3.9 months

期刊介绍： Includes reports on research, developments, and examinations performed by the Society''s members for the specific fields shown in the category list such as detailed below, the contents of which may advance the development of science and industry: (1) Reports on new theories, experiments with new contents, or extensions of and supplements to conventional theories and experiments. (2) Reports on development of measurement technology and various applied technologies. (3) Reports on the planning, design, manufacture, testing, or operation of facilities, machinery, parts, materials, etc. (4) Presentation of new methods, suggestion of new angles, ideas, systematization, software, or any new facts regarding the above.