Artículos de revistas
Complete Arcs Arising From A Generalization Of The Hermitian Curve
Registro en:
Acta Arithmetica. Instytut Matematyczny, v. 164, n. 2, p. 101 - 118, 2014.
651036
10.4064/aa164-2-1
2-s2.0-84907275495
Autor
Borges H.
Motta B.
Torres F.
Institución
Resumen
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. 164 2 101 118 Borges Filho, H., On complete (N d)-arcs derived from plane curves (2009) Finite Fields Appl., 15, pp. 82-96 Borges Filho, H., Conceic¸ão, R., (2013) Minimal Value Set Polynomials and a Generalization of the Hermitian Curve, , preprint Bulygin, S.V., Generalized Hermitian codes over GF(2r) (2006) IEEE Trans. Inform. Theory, 52, pp. 4664-4669 Çakc¸ak, E., Özbudak, F., Curves related to Coulter's maximal curves (2008) Finite Fields Appl., 14, pp. 209-220 Coulter, R.S., Explicit evaluations of some Weil sums (1998) Acta Arith., 83, pp. 241-251 Coulter, R.S., Further evaluations of Weil sums (1998) Acta Arith., 86, pp. 217-226 Coulter, R.S., On the evaluation of a class of Weil sums in characteristic 2 (1999) New Zealand J. Math., 28, pp. 171-184 Coulter, R.S., The number of rational points of a class of Artin-Schreier curves (2002) Finite Fields Appl., 8, pp. 397-413 Garcia, A., Özbudak, F., Some maximal function elds and additive polynomials (2007) Comm. Algebra, 35, pp. 1553-1566 Garcia, A., Stichtenoth, H., A class of polynomials over finite fields (1999) Finite Fields Appl., 5, pp. 424-435 Giulietti, M., Korchmáros, G., A new family of maximal curves over a finite field (2009) Math. Ann., 343, pp. 229-245 Giulietti, M., Pambianco, F., Torres, F., Ughi, E., On complete arcs arising from plane curves (2002) Des. Codes Cryptogr., 25, pp. 237-246 Hefez, A., Voloch, J.F., Frobenius nonclassical curves (1990) Arch. Math. (Basel), 54, pp. 263-273. , Correction, ibid. 57 (1991), 416 Hirschfeld, J.W.P., (1998) Projective Geometries over Finite Fields, 2nd Ed., , Oxford Univ. Press, Oxford Hirschfeld, J.W.P., Korchmáros, G., Torres, F., (2008) Algebraic Curves over a Finite Field, , Princeton Univ. Press, Princeton Hirschfeld, J.W.P., Voloch, J.F., The characterization of elliptic curves over finite fields (1988) J. Austral. Math. Soc. Ser. A, 45, pp. 275-286 Lidl, R., Niederreiter, H., Finite Fields (1983) Encyclopedia Math. Appl., 20. , Addison-Wesley, Reading, MA Munuera, C., Sepúlveda, A., Torres, F., Algebraic geometry codes from Castle curves (2008) Lecture Notes in Comput. Sci., 5228, pp. 117-127. , Springer, Berlin Munuera, C., Sepúlveda, A., Torres, F., Generalized Hermitian codes (2013) Des. Codes Cryptogr., 69, pp. 123-130 Stichtenoth, H., (1993) Algebraic Function Fields and Codes, , Springer, Berlin Tafazolian, S., A note on certain maximal hyperelliptic curves (2012) Finite Fields Appl., 18, pp. 1013-1016 Tsfasman, M.A., Vlədut¸, S.G., (1991) Algebraic-Geometric Codes, , Kluwer, Dordrecht Wolfmann, J., The number of points on certain algebraic curves over finite fields (1989) Comm. Algebra, 17, pp. 2055-2060