The dual of an evaluation code

The aim of this work is to study the dual and algebraic an evaluation code using standard monomials indicator functions. We show that dual. develop algorithm for computing a basis Let $C_1$ $C_2$ be linear codes spanned by monomials. give combinatorial condition monomial equivalence $C_2^\perp$. Moreover, we explicit description generator matrix $C_2^\perp$ in terms coefficients For Reed--Muller-type duality criterion v-number Hilbert function vanishing ideal. As application, provide corresponding Gorenstein ideals. In addition, when set points degenerate affine space, classify code.