Bounds on Spectra of Codes with Known Dual Distance
Designs, Codes and Cryptography
On the Distance Distributions of BCH Codes and Their Duals
Designs, Codes and Cryptography
Upper Bounds on the Dual Distance of BCH(255, k)
Designs, Codes and Cryptography
Performance analysis of linear codes under maximum-likelihood decoding: a tutorial
Communications and Information Theory
Long extended BCH codes are spanned by minimum weight words
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
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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.