Hugues Verdure

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Generalizing polynomials previously studied in the context of linear codes, we define weight polynomials and an enumerator for a matroid M . Our main result is that these polynomials are determined by Betti numbers associated with N0-graded minimal free resolutions of the Stanley-Reisner ideals of M and so-called elongations of M . Generalizing Greene’s(More)
To each linear code $$C$$ over a finite field we associate the matroid $$M(C)$$ of its parity check matrix. For any matroid $$M$$ one can define its generalized Hamming weights, and if a matroid is associated to such a parity check matrix, and thus of type $$M(C)$$ , these weights are the same as those of the code $$C$$ . In our main result we show how the(More)
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