More results on the weight enumerator of product codes
We consider the product code C-p of q-ary linear codes with minimum distances d(c) and d(r). The words in C-p of weight less than d(r)d(c) + max(d(r)[d(c)/g], d(c)[d(r)/q]) are characterized, and their number is expressed in the number of low weight words of the constituent codes. For binary product codes, we give an upper bound on the number of words in C-p of weight less than min(d(r)(d(c) + [d(c)/2] + 1), d(c)(d(r) + [d(r)/2] + 1)) that is met with equality if C-c and C-r are (extended) perfect codes.
weight enumerator product codes