The Weight Distributions of the (256, k) Extended Binary Primitive BCH Codes with k ≤ 71 and k ≥ 187

Abstract

Computing the weight distribution of a code is a challenging problem in coding theory. In this paper, the weight distributions of (256, k) extended binary primitive BCH codes with k ≤ 71 and k ≥ 187 are given. The weight distributions of the codes with k ≤ 63 and k ≥ 207 have already been obtained in our previous work. Affine permutation and trellis structure are used to reduce the computing time. Computer programs in C language which use recent CPU instructions, such as SIMD, are developed. These programs can be deployed even on an entry model workstation to obtain the new results in this paper.