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Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree

100%

Arakelian N., Borges H.

Acta Arithmetica

2015

tom 167

nr 1

43-66

For each integer s ≥ 1, we present a family of curves that are $𝔽_q$-Frobenius nonclassical with respect to the linear system of plane curves of degree s. In the case s=2, we give necessary and sufficient conditions for such curves to be $𝔽_q$-Frobenius nonclassical with respect to the linear system of conics. In the $𝔽_q$-Frobenius nonclassical cases, we determine the exact number of $𝔽_q$-rational points. In the remaining cases, an upper bound for the number of $𝔽_q$-rational points will follow from Stöhr-Voloch theory.

Complete arcs arising from a generalization of the Hermitian curve

81%

Borges H., Motta B., Torres F.

Acta Arithmetica

2014

tom 164

nr 2

101-118

We investigate complete arcs of degree greater than two, in projective planes over finite fields, arising from the set of rational points of a generalization of the Hermitian curve. The degree of the arcs is closely related to the number of rational points of a class of Artin-Schreier curves, which is calculated by using exponential sums via Coulter's approach. We also single out some examples of maximal curves.

Ograniczanie wyników

2 Acta Arithmetica

2 Borges H.

1 Arakelian N.

1 Motta B.

1 Torres F.

1 2015

1 2014

Wyniki wyszukiwania

Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree

Complete arcs arising from a generalization of the Hermitian curve