重根循环码的进一步研究

Further Study of Repeated-Root Cyclic Codes

给出了在有限域F_q上长度为N=p^s n的q-元重根循环码的生成多项式;证明了有限域F_q上长度为N=p^s n的q-元重根循环码等价于F_q上p^s个单根循环码的组合.

In the theory of cyclic codes,it is common practice to require(n,p)=1,where n is the word length and p is the characteristic of F_q.This ensures that the generator g(x)of the cyclic codes h~ no multiple zeros(repeated roots).In this paper,the generator of repeated-root is given.Moreover,q-ary repeated-root cyclic codes C of length N =p^s n can be combined with p^s cyclic codes.