Linear codes, arrangements, lattices, matroids and their associated polynomials

Relinde Jurrius, Technische Universiteit Eindhoven

A linear code gives rise to an arrangement of hyperplanes, to a matroid and to a geometric lattice. I will describe these objects and their connections. To all the objects several polynomials are associated, such as the weight enumerator of a linear code, the Tutte polynomial of a matroid and the characteristic polynomial of an arrangement or geometric lattice. The question arises naturally whether or not these polynomials determine each other. In most cases the answer is known, and I will give an overview of the relations.

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