Title :
Decoding geometric Goppa codes up to designed minimum distance by solving a key equation in a ring
Author :
Shen, B.-Z. ; Tseng, K.K.
Author_Institution :
Dept. of Comput. Sci. & Electr. Eng., Lehigh Univ., Bethlehem, PA, USA
fDate :
27 Jun-1 Jul 1994
Abstract :
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
Keywords :
Goppa codes; algebraic geometric codes; decoding; affine ring; algebraic-geometric codes; algorithm; decoding; designed minimum distance; equation; geometric Goppa codes; majority voting scheme; Algorithm design and analysis; Computer science; Decoding; Equations; Galois fields; Voting;
Conference_Titel :
Information Theory, 1994. Proceedings., 1994 IEEE International Symposium on
Conference_Location :
Trondheim
Print_ISBN :
0-7803-2015-8
DOI :
10.1109/ISIT.1994.394817