Decoding geometric goppa codes up to designed minimum distance by solving a key equation in a ring

A new algorithm is developed for decoding geometric Goppa codes (algebraic-geometric codes) up to their designed minimum distance, This algorithm is constructed on the basis of the one introduced by Porter, Shen, and Pellikaan, but has improved it considerably in decoding capability by incorporating a majority voting scheme conceptually analogous to that employed by the algorithms of Feng and Rao, and Duursma. The algorithm is distinct from others in that its major steps are accomplished by solving a key equation in an affine ring. The result is a new algorithm with decoding capability on a par with that of Feng and Rao's and Duursma's algorithms, The new algorithm is applicable to a large class of geometric Goppa codes and thus provides a viable alternative to the algorithms of Feng and Rao, as well as Duursma for decoding geometric Goppa codes up to designed minimum distance.