A tutorial on AG code construction from a Gröbner basis perspective

Abstract

This chapter is meant primarily as an introduction to AG codes, with material on producing proper one-point descriptions of these codes as well. The terminology chosen is that of the easily understood concepts of multivariate polynomial rings and ideals of relations among the variables, which is more useful computationally than the more standard algebraic geometry terminology. © 2009 Springer-Verlag Berlin Heidelberg.