Some results on the weight distributions of the binary double-circulant codes based on primes
- ISBN: 142440410X
- DOI: 10.1109/ICCS.2006.301431
Abstract
This paper presents a more efficient algorithm to count codewords of given weights in self-dual double-circulant and formally self- dual quadratic double-circulant codes over GF(2). A method of deducing the modular congruence of the weight distributions of the binary quadratic double-circulant codes is proposed. This method is based on that proposed by Mykkeltveit, Lam and McEliece, JPL. Tech. Rep., 1972, which was applied to the extended quadratic- residue codes. A useful application of this modular congruence method is to provide independent verification of the weight dis- tributions of the extended quadratic-residue and quadratic double- circulant codes. Using this method in conjunction with the pro- posed efficient codeword counting algorithm, we are able i) to give the previously unpublished weight distributions of the 76, 38, 12 and 124, 62, 20 binary quadratic double-circulant codes; ii) to provide corrections to the published results on the weight distri- butions of the binary extended quadratic-residue code of prime 151, and the number of codewords of weights 30 and 32 of the binary extended quadratic-residue code of prime 137; and iii) to prove that the 168, 84, 24 extended quadratic-residue and qua- dratic double-circulant codes are inequivalent.
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