A CODE DECOMPOSITION APPROACH FOR DECODING CYCLIC AND ALGEBRAIC-GEOMETRIC CODES

An approach based on code decomposition and partial transform for cons tructing algorithms for decoding cyclic codes and algebraic-geometric (AG) codes is introduced, A general decoding procedure applicable to a rbitrary linear codes and their subfield subcodes is then developed, I n particular, we have developed algorithms for error-and-erasure decod ing of cyclic codes up to their actual maximum distance, error-and-era sure decoding of AG codes up to their designed minimum distance, and d ecoding of subfield subcodes of AG codes (geometric BCH codes), Moreov er, a generalization of geometric BCH codes is introduced. It is shown by an example that for a simple class of AG codes, the so-called one- point codes, this generalization brings a better estimate of their min imum distance, It is also shown that the algorithms developed in this paper can be applied to decode these codes up to their estimated minim um distance.