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 (see IEEE Trans. Inform. Theory, vol.IT-38, p. 1663-1676, 1992), 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 (see IEEE Trans. Inform. Theory, vol.IT-39, p.505, 1993) and Duursma (see IEEE Trans. Inform. Theory, vol.IT-39, p.1067-1070, 1993). 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-Rao 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-Rao and Duursma for decoding geometric Goppa codes up to designed minimum distance