Groebner Bases and Coding
Thomas Risse · 2015
In the past Groebner bases have been proved to be a very potent tool to solve a variety of problems first of all in mathematics but also in science and engineering.Hence, it is near at hand to study application of Groebner bases in coding, i.e. the encoding and especially the decoding of linear error correcting codes.This paper attempts an overview focusing on Reed-Solomon codes and Goppa codes together with their coding and decoding algorithms.