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

Authors:
Darren Glass;David Joyner;Amy Ksir
Affiliations:
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
Venue:
International Journal of Information and Coding Theory
Year:
2010

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Abstract

Let Χ denote the hyperelliptic curve y² = x^p - 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.