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Let Χ denote the hyperelliptic curve y<SUP align=right>2</SUP> = x<SUP align=right>p</SUP> - 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.

Codes from Riemann-Roch spaces for y<SUP align=right>2</SUP> = x<SUP align=right>p</SUP> - x over GF(p)