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.
Recommended Citation
Matthews, Gretchen L., "Weierstrass Pairs and Minimum Distance of Goppa Codes." (1999). LSU Historical Dissertations and Theses. 6947.
https://repository.lsu.edu/gradschool_disstheses/6947
ISBN
9780599372566
Pages
50
DOI
10.31390/gradschool_disstheses.6947