Codes from Riemann-Roch spaces for y2 = xp - x over GF(p)
Darren Glass, David A. Joyner, Amy Ksir · International Journal of Information and Coding Theory · 2010
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.