计算机工程与应用 ›› 2014, Vol. 50 ›› Issue (18): 113-117.

• 网络、通信、安全 • 上一篇    下一篇

三元域上三次和四次剩余码的幂等生成元

董学东1,张  瑶2,张  妍2   

  1. 1.大连大学 信息工程学院,辽宁 大连 116622
    2.辽宁师范大学 数学学院,辽宁 大连 116029
  • 出版日期:2014-09-15 发布日期:2014-09-12

Generating idempotents of cubic and quartic residue codes over field [F3]

DONG Xuedong1, ZHANG Yao2, ZHANG Yan2   

  1. 1.College of Information Engineering, Dalian University, Dalian, Liaoning 116622, China
    2.School of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, China
  • Online:2014-09-15 Published:2014-09-12

摘要: 有限域上高次剩余码的生成多项式都是多项式[xn-1]的因式。针对多项式[xn-1]在有限域上分解的困难性,给出了三元域[F3]上三次和四次剩余码的幂等生成元表达式。利用计算机软件求解这些幂等生成元与[xn-1]最大公因式就可得到三次和四次剩余码生成多项式而不用分解[xn-1]。

关键词: 幂等生成元, 剩余码, 循环码

Abstract: The generating polynomials of higher degree residue codes over finite fields are factors of the polynomial[xn-1]. Generally speaking, it is difficult to factor the polynomial[xn-1] over finite fields. This paper gives generating idempotents of cubic and quartic residue codes over the field [F3]. As a result, the generating polynomials of cubic and quartic residue codes over the field [F3] can be obtained by computing the greatest common divisors of these generating idempotents and the polynomial[xn-1] with computer software such as Matlab and Maple.

Key words: generating idempotent, residue code, cyclic code