9406043 Tzeng This project is a program of research in the construction, analysis, and decoding of error control codes. The primary objective is the development to efficient error control coding techniques for reliable data transmission and storage. The specific areas of investigation are (1) developing algebraic methods for determining the maximum error-correcting capabilities of cyclic codes and algebraic-geometric (AG) codes; (2) constructing efficient algorithms for decoding cyclic and AG codes; (3) bridging the gap between the ;more traditional cyclic codes and the AG codes; and (4) developing efficient concatenated coding coding schemes using AG codes. For the determination of minimum distance, the project will develop an approach based on Newton's identities and their extensions. Closely related approaches based on the shifting method of van Lint and Wilson and the method of counting the number of"sentinels" in a syndrome matrix will be investigated. The techniques utilized will both lead to minimum distance determination and to a procedure for constructing algorithms capable of using the maximum error-correcting capabilities. Considerable is planned to develop links between cyclic and AG codes. Concatenated codes using convolutional codes as inner codes and AG codes as outer codes will also be studies. Both theoretical and practical issues will be addressed. ***
