一类循环码覆盖多项式个数的上界及其覆盖多项式的求取方法

An Upper Bound of the Number of Covering Polynomials for a Class of Cyclic Codes and the Method to Find the Covering Polynomials

Tadao Kasami提出了一种循环码的覆盖多项式译码法,该方法实现简单,速度也较快。但是,该方法的关键是寻求循环码的一个覆盖多项式集合。给定一个循环码,求取它的覆盖多项式集合目前尚无系统的方法。本文首先对循环码进行了分类,而后对Ⅱ-型循环码覆盖多项式的个数给出了一个上界,并且给出了一种具体求取Ⅱ-型循环码的覆盖多项式集合的一种方法。

Tadao Kasami[1] proposed a decoding method for cyclic codes. This method has higher speed and simple construction. The key point of this method is to find a set of covering polynomials. For a cyclic code, it is difficult to find the set of it's covering polynomials. We have not had a systematic method to find it. In this paper, we first classify the cyclic codes, then give a upper hound of the number of covering polynomials, and a method to find the set of the covering polynomials for the Ⅱ-type cyclic codes.