On Divisibility of Exponential Sums over Finite Fields of Characteristic 2
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.
KeywordsBoolean Function Polynomial Equation Finite Field Code Theory Covering Method
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- 5.G. Cohen, L. Honkala, S. Litsyn, and A. Lobstein, Covering Radius, 54, North-Holland Mathematical.Google Scholar
- 6.S. Litsyn, C.J. Moreno, and O. Moreno, Divisibility Properties and New Bounds for Exponential Sums in One Variable and Several Variables, AAECC J.,1994.Google Scholar
- 8.O. Moreno, A. Cáceres, and M. Alonso, An Improved and Simplified Binary Ax’s Theorem, Proceeding 1994 IEEE International Symposium on Information Theory, Trondheim, Norway 1994.Google Scholar
- 9.O. Moreno and F.N. Castro, and A. Cáceres, Exponential Sums in Several Variables over Finite Fields, Coding Theory, Cryptography and Related Areas, pp 209–220.. Springer. 2000.Google Scholar
- 10.O. Moreno, and F. N. Castro, Comparison of Thechniques on Divisibility Properties of Exponential Sums and Applications, Finite Fields, and Applications,pp 363–389, Springer, 2001.Google Scholar
- 12.O. Moreno, and C. J. Moreno, The MacWilliams-Sloane Conjecture on the Tightness of Carlitz-Uchiyama Bound and the Weights of Duals of BCH Codes, IEEE Trasactions on Information Theory, 40, no. 6, 1994.Google Scholar