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Abstract

This research project involves an investigation of error correcting codes. The safe and reliable transfer of information depends on coding theory. The problem of transferring dependable information is important and this research project attempts to continue incremental progress in the field. Specifically, the project will emphasize formally self dual codes and will expand upon Duursma's ideas in Extremal Weight Enumerators and Ultraspherical Polynomials. Considerable work has been devoted to the study of self dual codes. Iwan M. Duursma has written numerous papers on the matter and the greater part of this project is centered on his work. In 1999, Iwan M. Duursma defined the zeta function for a linear code as a generating function of its Hamming weight enumerator. The modest goal of Midn Catalano's project is to go through Duursma's papers and evaluate its relevance for formally self dual codes. Therefore, the research projects aims to extend Duursma's work in Extremal Weight Enumerators and Ultraspherical Polynomials to formally self dual codes. More specifically, the project expands Duursma's work to zeta functions of formally self dual codes of Type IV.

Author Bio

Sarah Catalano attended the United States Naval Academy from June 2004 to May 2008. She is a member of the Class of 2008 and earned a Bachelors of Science Degree in Mathematics. As part of her honors course work, she did research in coding theory, specifically looking at Duursma Zeta Functions of Type IV Virtual Codes. Upon graduation, she will attend the Naval Postgraduate School in Monterey, CA, where she will be working towards a Masters of Science degree in Joint Command, Control, Communications, and Intelligence.

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