Gröbner Bases Methods in Coding Theory
Cícero Carvalho · Contemporary mathematics - American Mathematical Society · 2015
This is the text of a short course given at the ASReCoM meeting, in Morelia, Mexico. We introduce the theory of Gröbner bases with emphasis on the concept of footprint of an ideal. After presenting some results which relate the footprint to the number of points in an affine variety, we introduce the concepts of affine variety code, and a particular case of it, the so-called affine cartesian codes. We then proceed to determine the parameters of such codes. These parameters were recently calculated by López, Rentería-Marquez and Villareal but our calculation, which uses properties of the fooprint, is different from theirs.