Códigos duais de códigos de avaliação - Gomes, Lucas Vinnicius de Oliveira (2023)
We start this work by presenting the theory of Gröbner bases with emphasis on the concept of the footprint of an ideal. Then we introduce the concepts of affine evaluation code and the algebraic dual. After presenting the concepts of indicator functions and of mononomially equivalent codes, we start the study of monomial codes and their duals. The main result proves that the dual of a monomial code is monomially equivalent to a monomial code. At the end of this work we study an specific example of codes on the degenerate torus.