Title :
The weight hierarchy of product codes
Author :
Schaathun, Hans Georg
Author_Institution :
Dept. of Inf., Bergen Univ., Norway
fDate :
11/1/2000 12:00:00 AM
Abstract :
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
Keywords :
linear codes; set theory; Segre embedding; coordinate positions; linear code; minimum weight; minimum weights; product codes; projective multiset; projective systems; subcode; weight hierarchy; Informatics; Linear code; Product codes; Tensile stress; Vectors;
Journal_Title :
Information Theory, IEEE Transactions on
