Decoding Algebraic Geometry Codes by a Key Equation

A new effective decoding algorithm is presented for arbitrary algebraic-geometric codes on the basis of solving a generalized key equation with the majority coset scheme of Duursma. It is an improvement of Ehrhard's algorithm, since the method corrects up to half of the Goppa distance with complexity order $\text{O}$(n^2.81), and with no further assumption on the degree of the divisor G.