Uniqueness of low genus optimal curves over F_2

Alessandra Rigato

Uniqueness of low genus optimal curves over F_2

Number Theory 2010-05-26 v1

Authors: Alessandra Rigato

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.

Keywords

optimal curves genus finite field uniqueness algebraic curves F_2

Cite

@article{arxiv.1005.4591,
  title  = {Uniqueness of low genus optimal curves over F_2},
  author = {Alessandra Rigato},
  journal= {arXiv preprint arXiv:1005.4591},
  year   = {2010}
}

Comments

21 pages

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