Date of Award

12-2009

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Mathematical Science

Advisor

Matthews, Gretchen

Committee Member

Calkin , Neil

Committee Member

Gao , Shuhong

Committee Member

Xue , Hui

Abstract

Algebraic geometry codes have been studied greatly since their introduction by Goppa . Early study had focused on algebraic geometry codes CL(D;G) where G was taken to be a multiple of a single point. However, it has been shown that if we allow G to be supported by more points, then the associated code may have better parameters. We call such a code a multipoint code and if G is supported by m points, then we call it an m-point code. In this dissertation, we wish to develop a decoding algorithm for multipoint codes. We show how we can embed a multipoint algebraic geometry code into a one-point supercode so that we can perform list decoding in the supercode. From the output list, we determine which of the elements is a codeword in the multipoint code. In this way we have unique decoding up to the minimum distance for multipoint algebraic geometry codes, provided the parameters of the list decoding algorithm are set appropriately.

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