Title: Codes from Riemann-Roch spaces for y2 = xp - x over GF(p)

Authors: Darren Glass, David Joyner, Amy Ksir

Addresses: Department of Mathematics, Gettysburg College, Gettysburg, PA, USA. ' Department of Mathematics, United States Naval Academy, Annapolis, MD, USA. ' Department of Mathematics, United States Naval Academy, Annapolis, MD, USA

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.

Keywords: hyperelliptic curves; AG codes; SL(2,p) representations; Riemann-Roch spaces; automorphisms; automorphism groups; code structure.

DOI: 10.1504/IJICOT.2010.032545

International Journal of Information and Coding Theory, 2010 Vol.1 No.3, pp.298 - 312

Published online: 06 Apr 2010 *

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