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 (algeb raic-geometric codes) up to their designed minimum distance, This algo rithm is constructed on the basis of the one introduced by Porter, She n, and Pellikaan, but has improved it considerably in decoding capabil ity by incorporating a majority voting scheme conceptually analogous t o that employed by the algorithms of Feng and Rao, and Duursma. The al gorithm is distinct from others in that its major steps are accomplish ed by solving a key equation in an affine ring. The result is a new al gorithm 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 c lass of geometric Goppa codes and thus provides a viable alternative t o the algorithms of Feng and Rao, as well as Duursma for decoding geom etric Goppa codes up to designed minimum distance.