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The weight of a code is the number of coordinate positions where no codeword is zero. The th minimum weight is the least weight of an -dimensional subcode. Wei and Yang gave a conjecture about the minimum weights for some product codes. In this correspondence, we 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. Index Terms-Product code, projective system (projective multiset), Segre embedding, weightdoi:10.1109/18.887876 fatcat:7bdifbhudvanlabixjndmsheum