Document Type
Article
Publication Date
4-7-2010
Department 1
Mathematics
Abstract
Let Χ denote the hyperelliptic curve y2 = xp - x over a field F of characteristic p. The automorphism group of Χ is G = PSL(2, p). Let D be a G-invariant divisor on Χ(F). We compute explicit F-bases for the Riemann-Roch space of D in many cases as well as G-module decompositions. AG codes with good parameters and large automorphism group are constructed as a result. Numerical examples using GAP and SAGE are also given.
Copyright Note
This is the author's version of the work. This publication appears in Gettysburg College's institutional repository by permission of the copyright owner for personal use, not for redistribution.
DOI
10.1504/IJICOT.2010.032545
Version
Post-Print
Recommended Citation
Glass, Darren B., David Joyner, and Amy Ksir. "Codes from Riemann-Roch Spaces for Y2 = Xp - X over GF(P)." International Journal of Information and Coding Theory 1, no. 3 (2010): 298-312.
Required Publisher's Statement
This article was originally published on the publisher's website: https://www.inderscienceonline.com/doi/abs/10.1504/IJICOT.2010.032545