Minimum Distance Decoding of General Algebraic Geometry Codes via Lists
Nathan Drake, Gretchen L. Matthews · IEEE Transactions on Information Theory · 2010
Algebraic geometry codes are defined by divisorsDandGon a curve over a finite field F. Often,Gis supported by a single F-rational point and the resulting code is called a one-point code. Recently, there has been interest in allowing the divisorGto be more general as this can result in superior codes. In particular, one may obtain a code with better parameters by allowingGto be supported bymdistinct F-rational points, wherem> 1. In this paper, we demonstrate that a multipoint algebraic geometry codeCmay be embedded in a one-point codeC'. Exploiting this fact, we obtain a minimum distance decoding algorithm for the multipoint codeC. This is accomplished via list decoding in the one-point code C'.