Which families of long binary linear codes have a binomial weight distribution?
In this paper, primitive binary BCH-codes and two linear binary code families based on Hadamard matrices are considered. A review of all results concerning bounds on weight distributions of primitive binary BCH-codes is given in which it is stated that weights of long primitive binary BCH-codes are not binomially distributed. The weight distributions of some particular codes of the last two families are calculated and compared to the values of corresponding binomial distributions. Based on these results the family of binary doubly even self dual codes based on Hadamard matrices seems to be a good candidate to have binomially distributed weights for large code length, i. e., is a good candidate for an asymptotically optimal code family on the binary symmetric channel when decoded by a Maximum-Likelihood-Decoder with all codewords having equal prior probabilities.
KeywordsWeight Distribution Code Rate Block Code Dual Code Hadamard Matrice
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