一类最小距离为4的三元最优循环码
A Class of Ternary Optimal Cyclic Codes with Minimum Distance 4
DOI: 10.12677/pm.2024.148298, PDF,    科研立项经费支持
作者: 曾学强：四川轻化大学数学与统计学院，四川 自贡；何 潮：四川职业技术学院教师教育学院，四川 遂宁
关键词: 有限域；循环码；不可约多项式；最小距离；Finite Field； Cyclic Code； Irreducible Polynomial； Minimum Distance
摘要: 循环码作为线性码的一个重要子类，具有良好的通信性质和重要的应用意义。利用有限域上因式分解、低次不可约多项式的解等数学工具，从循环码生成多项式的角度研究具有两个零点的三元循环码，得到了一类最小距离为4的三元循环码，并且它们关于Sphere-Packing界是最优的。
Abstract: As an important subclass of linear codes, cyclic code has good communication properties and important application significance. By using mathematical tools such as factorization over finite field, solutions of low order irreducible polynomial, ternary cyclic code with two zeros are studied from the perspective of generating polynomials of cyclic code. A class of ternary cyclic code with minimum distance of 4 is obtained, and it is optimal with respect to Sphere Packing bounds.
文章引用：曾学强, 何潮. 一类最小距离为4的三元最优循环码[J]. 理论数学, 2024, 14(8): 12-19. https://doi.org/10.12677/pm.2024.148298

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