Properties of quasi-uniform codes

Quasi-uniform random variables have probability distributions that are uniform over their supports. They are of fundamental interest because a linear information inequality is valid if and only if it is satisfied by all quasi-uniform random variables. In this paper, we investigate properties of codes induced by quasi-uniform random variables.We prove that quasi-uniform codes (which include linear and almost affine codes as special cases) are distance-invariant and that Greene's Theorem and the Critical Theorem of Crapo and Rota hold in the setting of quasi-uniform codes. We also outline how these results provide a coding theoretic approach to construct information inequalities.