Códigos cartesianos afins com dual complementar - Santos, Pedro Augusto Diniz (2024)
In this work we carry out the study of Generalized Affine Cartesian Linear Codes with Complementary Dual. We introduce affine Cartesian codes, Reed-Muller codes, Reed-Solomon codes and their generalization. Using relationships between affine varieties and the footprint of an ideal, it was possible to determine the parameters of a code: dimension, minimum distance and length. Finally, we study conditions to determine whether a Cartesian code has the LCD property. Keywords: cartesian codes, lcd codes, footprint and Gröbner bases.