| 摘要: |
| 本文研究了基于有限域上的置换多项式构造置换码的问题.利用有限域上形如f(x)=αxm+βx(其中m为正整数)的置换多项式簇, 构造了五类置换码,并借助求解有限域上代数方程的一些方法,确定了这五类置换码的参数, 包括码长、码字数量和极小汉明距离, 所得结果丰富了置换码的构造理论. |
| 关键词: 置换多项式 置换码 极小汉明距离 码字数量 有限域 |
| DOI： |
| 分类号:O157.4;O153.4 |
| 基金项目:国家自然科学基金资助项目(62171479);中南民族大学中央高校基本科研业务费专项资金项目(CZZ25008). |
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| CONSTRUCTION AND PARAMETER ANALYSIS OF FIVE CLASSES OF PERMUTATION CODES FROM PERMUTATION POLYNOMIAL CLUSTERS |
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YE Na, XIA Yong-bo
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College of Mathematics and Statistics, South-Central Minzu University, Wuhan 430074, China
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| Abstract: |
| This paper investigates the construction of permutation codes based on the permutation polynomials over finite fields. By utilizing some permutation polynomials of the form f(x) = αxm + βx (where m is a positive integer) over finite fields, five classes of permutation codes are constructed. Employing some techniques of solving equations over finite fields, the parameters of these codes are determined, including the code length, cardinality, and minimum Hamming distance. The obtained results enrich the theory about the construction of permutation codes. |
| Key words: permutation polynomial permutation code minimum Hamming distance cardinality Finite field |
