A note on certain maximal hyperelliptic curves
Copyright policy )A note on certain maximal hyperelliptic curves
In this paper, the author gives necessary and sufficient conditions for a hyperelliptic curve of the form \(y^2=x^m+x\) to be maximal. More precisely, he proves that the curve \(y^2=x^{2g+1}+x\) is maximal over \(\mathbb{F}_{q^2}\) if and only if \(q\equiv -1\) or \(2g+1\pmod{4g}\), and the curve \(y^2=x^{2g+2}+x\) is maximal over the same field if and only if \(2g+1\) divides \(q+1\).
- Institute for Research in Fundamental Sciences Iran (Islamic Republic of)
Curves over finite and local fields, Finite ground fields in algebraic geometry, hyperelliptic curves, maximal curves, Maximal curves, Finite fields, finite fields, Hyperelliptic curves
Curves over finite and local fields, Finite ground fields in algebraic geometry, hyperelliptic curves, maximal curves, Maximal curves, Finite fields, finite fields, Hyperelliptic curves
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