eSeminar: The dual of an evaluation code

In this talk we study the dual and the algebraic dual of an evaluation code using standard monomials and indicator functions. We show that the dual of an evaluation code is the evaluation code of the algebraic dual. Given linear codes C1 and C2 spanned by standard monomials, we describe a combinatorial condition to determine if C2 is monomially equivalent to the dual of C1. Moreover, we give an explicit description of a generator matrix of the dual of C_1 in terms of that of C_1 and coefficients of indicator functions. This is a joint work with Ivan Soprunov and Rafael H. Villarreal.