Counting polynomials for linear codes, hyperplane arrangements, and matroids
Counting polynomials for linear codes, hyperplane arrangements, and matroids
Thomas-decomposition of a polynomial systems and the resulting counting polynomials are applied to the theory of linear codes, hyperplane arrangements, and vector matroids to reinterpret known polynomials such as characteristic polynomials and weight enumerator, to introduce a new polynomial counting the matrices defining the same matroid, and to introduce the …