Parameterized affine codes (Q2859348)

The authors study affine codes parametrised by monomials and their projective form. The main point is to compute the dimension, the length and the minimum distance of these codes using Gröbner bases. It is shown that these basic parameters coincide for the affine and the projective form of such a code and that the first two parameters can be expressed in terms of the Hilbert function and the degree of the homogeneous vanishing ideal. In particular, the basic parameters are computed for the case that the code comes from an affine torus. Finally, the authors present an implementation of their results in Macaulay 2.