Off-campus UNL users: To download campus access dissertations, please use the following link to log into our proxy server with your NU ID and password. When you are done browsing please remember to return to this page and log out.
Non-UNL users: Please talk to your librarian about requesting this dissertation through interlibrary loan.
Decoding algorithms for algebraic geometric codes over rings
Abstract
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 [special characters omitted]/pr[special characters omitted] where p is a prime, with respect to the squared Euclidean weight.
Subject Area
Mathematics
Recommended Citation
Bartley, Katherine, "Decoding algorithms for algebraic geometric codes over rings" (2006). ETD collection for University of Nebraska-Lincoln. AAI3208054.
https://digitalcommons.unl.edu/dissertations/AAI3208054