The weight hierarchy of product codes

The weight of a code is the number of coordinate positions where no codeword is zero. The rth minimum weight d/sub r/ is the least weight of an r-dimensional subcode. Wei and Yang (1993) gave a conjecture about the minimum weights for some product codes. In this article, we find a relation between product codes and the Segre embedding of a pair of projective systems, and we use this to prove the conjecture.