A correction and improvements of some recent results on walsh transforms of gold type and Kasami-Welch type functions

Coşgun A., ÖZBUDAK F.

6th International Workshop on Arithmetic of Finite Fields, WAIFI 2016, Ghent, Belgium, 13 - 15 July 2016, pp.243-257 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume:
  • Doi Number: 10.1007/978-3-319-55227-9_17
  • City: Ghent
  • Country: Belgium
  • Page Numbers: pp.243-257
  • Keywords: Finite fields, Gold type functions, Kasami-Welch type functions, Walsh transform

Abstract

We give explicit evaluations of Walsh transforms of Gold type functions f(x) = Tr-K (x(2a +1) + x(2b +1)), 0 <=< a < b when gcd (b - a, k) = gcd (b + a, k) and Kasami-Welch type functions f (x) = Tr-K (2(ta+1)/x(2a +1)), when t is odd, gcd (2(k) - 1,2(a) + 1) = 1, k is even. Therefore we correct a recent result of Roy'2012, we solve an open problem stated in Roy'2012 and we improve and generalize some results of Roy'2012 and Lahtonen-McGuire-Ward'2007.