On the Efficient Codewords Counting Algorithm and the Weight Distributions of the Binary Quadratic Double-Circulant Codes

Abstract

An efficient algorithm to count all code- words of given weight and a method to deduce the modular congruence of the weight distributions of the binary quadratic double-circulant codes are pre- sented. Using this algorithm, we give the weight dis- tribution of the quadratic double-circulant code of length 168 and that of the extended quadratic-residue code of the same length. The weight distributions of these two inequivalent codes of length 168, which were previously unknown, are independently verified and proved to be accurate using the modular congruence method.