Decoding Algebraic Geometry codes by a key equation

摘要

A new effective decoding algorithm is presented for arbitraryalgebraic-geometric codes on the basis of solving a generalized key equationwith the majority coset scheme of Duursma. It is an improvement of Ehrhard'salgorithm, since the method corrects up to the half of the Goppa distance withcomplexity order O(n**2.81), and with no further assumption on the degree ofthe divisor G.