On computing the number of code words with minimum weight for cyclic codes

The weight distribution is an important parameter that determines the performance of a code. The minimum distance and the number of corresponding codes that can be derived from the weight distribution, greatly affect the performance of the code. The decoding error probability and other performance measures can be calculated approximately from these. When the number of information points is increased, however, it becomes difficult in general to derive the weight distribution of the code. When the number of check points is increased, it also becomes difficult to derive the weight distribution of the original code word from the dual code. Thus, it is an important issue to reduce computational complexity in the derivation of the weight distribution. It is desired to develop a method that can derive the weight distribution with high speed, or the minimum distance and the number of corresponding code words. Recently, Barg and Dumer [5] proposed a method in which the minimum distance and the number of corresponding code words are determined efficiently, by utilizing the properties of the cyclic code. Even if their method is employed, however, a drastic improvement cannot be expected when the parameters are such that the number of information points is very large, since the number of code searches is not drastically reduced. This paper examines the properties of the cyclic code as well as the method of Barg-Dumer in further detail, and proposes a method that determine: efficiently the minimum distance and the number of corresponding code words with higher speed. The proposed method is compared to the method of Barg-Dumer through several numerical experiments, and the usefulness of the proposed method is demonstrated. The conditions under which the proposed methods are effective are investigated. (C) 1998 Scripta Technica.