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On Divisibility of Exponential Sums over Finite Fields of Characteristic 2

In: Finite Fields with Applications to Coding Theory, Cryptography and Related Areas

Author

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  • F. N. Castro

    (University of Puerto Rico, Department of Mathematics)

  • O. Moreno

    (University of Puerto Rico, Department of Mathematics)

Abstract

Moreno-Moreno’s result and the covering method give estimates on the 2-divisibility of the number of solutions of a system of polynomial equations. Let us call μ the order of the 2-divisibility given by Moreno-Moreno’s result and μ′ that of the covering method. In 2000 we proved that μ′ ≥ μ. In this present paper we give general conditions under which μ′ > μ. We also give some results concerning the tightness of the covering method.

Suggested Citation

  • F. N. Castro & O. Moreno, 2002. "On Divisibility of Exponential Sums over Finite Fields of Characteristic 2," Springer Books, in: Gary L. Mullen & Henning Stichtenoth & Horacio Tapia-Recillas (ed.), Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, pages 70-79, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-59435-9_5
    DOI: 10.1007/978-3-642-59435-9_5
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