Weierstrass Pairs and Minimum Distance of Goppa Codes

We prove that elements of the Weierstrass gap set of a pair of points may be used to define a geometric Goppa code which 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 particular codes defined using a linear combination of the two points.

• Type: Conference
• Year: 2001
• Where: DCC
• Authors: Gretchen L. Matthews
• Keywords: Computer Graphics, DCC 2001, Usual Lower Bound, Weierstrass Gap Set, Weierstrass Points