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The weight hierarchy of product codes

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1 Author(s)
Georg Schaathun, Hans ; Dept. of Inf., Bergen Univ., Norway

The weight of a code is the number of coordinate positions where no codeword is zero. The rth minimum weight dr 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

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Information Theory, IEEE Transactions on  (Volume:46 ,  Issue: 7 )