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Algebraic curves over finite fields


This project aims to obtain and characterizenew algebraic curves over finite fields and with many rational points. It also includes the study of a very special class of polynomials that, despite of being interesting on its own,turned out to be the key ingredient in the study of Frobenius non-classical curves. The arc property of curves attaining the Hasse-Weil boundis also considered in our study. Application in Coding Theory is one of the motivations of this work. (AU)

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Scientific publications (4)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
BORGES, HERIVELTO; MOTTA, BEATRIZ; TORRES, FERNANDO. Complete arcs arising from a generalization of the Hermitian curve. ACTA ARITHMETICA, v. 164, n. 2, p. 101-118, . (11/19446-3)
ARAKELIAN, NAZAR; BORGES, HERIVELTO. Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree. ACTA ARITHMETICA, v. 167, n. 1, p. 43-66, . (11/19446-3, 13/00564-1)
BORGES, HERIVELTO; CONCEICAO, RICARDO. On the characterization of minimal value set polynomials. JOURNAL OF NUMBER THEORY, v. 133, n. 6, p. 2021-2035, . (11/19446-3)
BORGES, HERIVELTO. Frobenius nonclassical components of curves with separated variables. JOURNAL OF NUMBER THEORY, v. 159, p. 402-425, . (11/19446-3)

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