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_rd_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 weightless 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.