Weight Distributions of Cyclic Self-Dual Codes


Carmen-Simona Nedeloaia

INRIA, projet CODES
and University of Limoges, LACO.
carmen.nedeloaia@unilim.fr

IEEE Transactions on Information Theory, vol 49, no 6, June 2003, pp. 1582-1591.


Abstract

We give a 1-level squaring construction for binary repeated-root cyclic codes of length n=2^ab where a is greater than 1 and b is odd. This allows us to obtain the weight distributions of all cyclic binary self-dual codes of lengths up to 110, which are not accessible by direct computation. We also use the shadow construction, as a particular method for Type I self-dual codes.

Keywords

Cyclic codes, self-dual codes, shadow codes, squaring construction, \uv construction, weight enumerator.