Decoding algorithms for algebraic geometric codes over rings

Algebraic geometric codes over rings were defined and studied in the late 1990's by Walker, but no decoding algorithm was given. In this dissertation, we present three decoding algorithms for algebraic geometric codes over rings.; The first algorithm presented is a modification of the basic algorithm for algebraic geometric codes over fields, and decodes with respect to the Hamming weight. The second algorithm presented is a modification of the Guruswami-Sudan algorithm, a list decoding algorithm for one-point algebraic geometric codes over fields. This algorithm also decodes with respect to the Hamming weight. Finally, we show how the Koetter-Vardy algorithm, a soft-decision decoding algorithm, can be used to decode one-point algebraic geometric codes over rings of the form Z /pr Z where p is a prime, with respect to the squared Euclidean weight.