The Principle Investigator (PI) will conduct research in the analysis of good error-correcting codes and the construction of practical decoding algorithms. The primary objective is to develop efficient error-control techniques for improving data integrity in digital communications and computer storage systems. The specific research problems include: (1) the investigation of the minimum distance structure of Goppa codes and generalized Goppa codes to obtain lower bounds comparable to those known for cyclic codes; (2) to resolve the problem of decoding those cyclic codes with minimum distance bounded by the Roos or Van Lint-Wilson bounds using the multiple syndrome sequences available to these codes and (3) to develop procedures for decoding Goppa codes and generalized Goppa codes up to the new bounds obtained in part (1).
