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arXiv · 1005.4591

Uniqueness of low genus optimal curves over F_2

Alessandra Rigato
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Abstract

A projective, smooth, absolutely irreducible algebraic curve X of genus g defined over a finite field F_q is called optimal if for every other such genus g curve Y over F_q one has $\#Y(F_q)\le \#X(F_q)$. In this paper we show that for $g\le 5$ there is a unique optimal genus g curve over F_2. For g=6 there are precisely two and for g=7 there are at least two.

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Alessandra Rigato. 2010-05-25. Uniqueness of low genus optimal curves over F_2. https://arxiv.org/abs/1005.4591

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