9305038 Welch This project is an investigation of decoding procedures for cyclic codes and algebraic geometry (AG) codes with the following objectives: 1. To obtain efficient and fast decoding procedures for the decoding of cyclic codes up to the best known lower bound of the minimum distance and to achieve the decoding of binary cyclic codes of considerable lengths (for example codes of lengths less than 255) up to the actual minimum distance. 2. To achieve the decoding of AG codes up to the designed minimum distance with complexities to rival those of BCH codes and Reed Solomon codes G. L. Feng will be a post-doctoral researcher on the project. The investigators have shown a universal method of determining the minimum lower distance bounds. The have investigated the possibility of decoding linear codes of considerable length up to the bound obtained and decoding binary cyclic codes up to their actual minimum distance using a generalized majority scheme. They have discussed the modified Gauss elimination for Hankel matrix and block-Hankel matrix which may result in lower complexity in the decoding of AG codes. These algorithms will be investigated in order to reduce the complexities. ***
