Date of Award

1999

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

First Advisor

Robert F. Lax

Abstract

We prove that elements of the Weierstrass gap set of a pair of points may be used to define a geometric Goppa code that has minimum distance greater than the usual lower bound. We determine the Weierstrass gap set of a pair of any two Weierstrass points on a Hermitian curve and use this to increase the lower bound on the minimum distance of certain codes defined using a linear combination of the two points. In particular, we obtain some two-point codes on a Hermitian curve that have better parameters than the one-point code on this curve with the same dimension. These results generalize to certain codes defined using an m-tuple of points on a smooth projective absolutely irreducible curve.

ISBN

9780599372566

Pages

50

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