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(r) is the least weight of an r-dimensional subcode. Wei and Yang gave a conjecture about the minimum weights for some product codes. In this correspondence,,ve will find a relation between product codes and the Segre embedding of a pair of projective systems, and we use this to prove the conjecture.
weight hierarchy product code segre embedding projective system (projective multiset)