An approximation to the weight distribution of binary linear codes

Binary primitive BCH codes form a large class of powerful error-correcting codes. The weight distributions of primitive BCH codes are unknown except for some special classes, such as the single, double, triple error-correcting codes and some very low-rate primitive BCH codes. However, asymptotic results for the weight distribution of a large subclass of primitive BCH codes have been derived by Sidel´nikov. These results provide some insight into the weight structure of primitive BCH codes. Sidel´nikov´s approach is improved and applied to the weight distribution of any binary linear block code. Then Sidel´nikov´s results on the weight distributions of binary primitive BCH codes are improved and it is shown that the weights of a binary primitive code have approximate binomial distribution.