Decoding algebraic-geometric codes up to the designed minimum distance

Abstract

A simple decoding procedure for algebraic-geometric codes C/sub Omega /(D,G) is presented. This decoding procedure is a generalization of Peterson's decoding procedure for the BCH codes. It can be used to correct any ((d*-1)/2) or fewer errors with complexity O(n/sup 3/), where d* is the designed minimum distance of the algebraic-geometric code and n is the codelength.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>