New bounds on the maximum number of points on genus-4 curves over small finite fields

Details New bounds on the maximum number of points on genus-4 curves over small finite fields New bounds on the maximum number of points on genus-4 curves over small finite fields

2011-08-26

arxiv.org/abs/1108.5393v4

Mathematics

Algebraic Geometry

18 pages. Differences from preceding version: Did some general copyediting; fixed broken links; added argument for a case that

Scientific paper

For prime powers q<100, we compute new upper and lower bounds on N_q(4), the
maximal number of points on a genus-4 curve over a finite field with q
elements. We determine the exact value of N_q(4) for 17 prime powers q for
which the value was previously unknown.

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