Weight distribution of cosets of 2-error-correcting binary BCH codes of length 15, 63 and 255

The weight distributions of cosets are not known for the class of binary 2-error-correcting BCH codes of length n=2^m-1, m even (the nonuniformly packed case). By using the graph theoretical concepts of the combinatorial matrix of a code and an r-partition design introduced in previous works, the authors obtain these distributions of cosets in the three particular cases of length 15, 63, and 255. It is observed that in these three cases the number of distinct weight distributions is a constant equal to 8