重根循环码

Repeated-root Cyclic Codes

在循环码理论中,通常要求码字的长度n与有限域Fq的特征p互素,即(n,p)=1,这样才能保证循环码的生成多项式g(x)没有重根。使用离散傅里叶变换(DFT),得到长度为N=psn的q—元重根循环码的谱表示和重根循环码的结构,这对重根循环码的构造及译码有重要作用。

In the theory of cyclic codes, it is common practice to require the （n,p） = 1, where n is the word length and p is the characteristic of Fq. This ensures that the generator g（x） of the cyclic codes has no muhiple zeros （ repeated roots）. In this paper, using the discrete fourier transforms, we describe the structure of q-ary repeated-root cyclic codes C of length N =p＇n.