二元域上三次和四次剩余码的幂等生成元

Generating idempotents of cubic and quartic residue codes over field F_2

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,给出了二元域F2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该幂等生成元与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。

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 Xxn - 1 over finite fields. This paper gives generating idempotents of cu- bic and quartic residue codes over the field F2 . As a result, the generating polynomials of cubic and quartic residue codes over the field F2 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 .