FGLM-like decoding: From Fitzpatrick's approach to recent developments

Abstract

Many decoding problems in algebraic coding theory can be solved by the computation of a suitable Gröbner basis. The Gröbner basis can often be computed via the FGLM algorithm or a related algorithm (like the Buchberger-Möller algorithm). In this tutorial we describe how this has been done in the literature from a historical point of view, starting from Fitzpatrick's seminal 1995 paper, and covering recent developments for list decoding. © 2009 Springer-Verlag Berlin Heidelberg.