ESTIMATION OF SOME EXPONENTIAL SUM BY MEANS OF q-DEGREE

Valérie Gillot (1) , Philippe Langevin (1)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134

In this paper, we improve results of Gillot, Kumar and Moreno to estimate some exponential sums by means of q-degrees. The method consists in applying suitable elementary transformations to see an exponential sum over a finite field as an exponential sum over a product of subfields in order to apply Deligne bound. In particular, we obtain new results on the spectral amplitude of some monomials.

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Valérie Gillot, Philippe Langevin. ESTIMATION OF SOME EXPONENTIAL SUM BY MEANS OF q-DEGREE. Glasgow Mathematical Journal, 2010, 52, pp.315--324. ⟨10.1017/S0017089510000017⟩. ⟨hal-00993148⟩