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.
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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.
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This article was originally published on the publisher's website: https://www.inderscienceonline.com/doi/abs/10.1504/IJICOT.2010.032545
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