Hamming weights and Betti numbers of Stanley-Reisner rings associated to matroids

Published 16 Aug 2011 in math.CO | (1108.3172v2)

Abstract: To each linear code over a finite field we associate the matroid of its parity check matrix. We show to what extent one can determine the generalized Hamming weights of the code (or defined for a matroid in general) from various sets of Betti numbers of Stanley-Reisner rings of simplicial complexes associated to the matroid.

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