The Weight Distributions of Some Binary Quadratic
Residue Codes

Yaotsu Chang
Department of Applied Mathematics
I-Shou University
Taiwan

Abstract    Full Text PDF

The weight distributions of binary quadratic residue codes C can be obtained by calculating certain subsets with sizes one-fourth of C. This result can be further improved to one-eighth when the code lengths of C are congruent to 7 modulo 8. An algorithm to determine the weight distributions of binary cyclic codes is given. As a consequence, the weight distributions of (73, 37, 13), (89, 45, 17), and (97, 49, 15) quadratic residue codes are determined precisely; they are new.