Weight Distribution of Some Cyclic Codes of MacWilliams
Mrs. MacWilliams recently gave methods for the decomposition of cyclic codes of block lengths 3p, 5p, and 7p into systematic quasi-cyclic form. In this paper, using her results, we construct and enumerate the complete weight distribution of many cyclic codes. Among the many codes, exhibiting remarkable gaps in their weight distributions are the (87,28,24), (51,16,16) and the (91,12,36) codes with weights divisible by four, and a (85,16,32) code with weights divisible by eight. We also report on a (52,13, 16) quasi-cyclic subcode (of the (65,13,25) cyclic code) with all weights divisible by four. It is not known if this code is cyclic as well.
Unable to display preview. Download preview PDF.
- (1).MacWilliams, F.J.: 1979, “Decomposition of cyclic codes of block lengths 3p,5p,7p”, IEEE Trans on Info. Theory, 25,Google Scholar