Explicit evaluation of Walsh transforms of a class of Gold type functions


Cosgun A.

FINITE FIELDS AND THEIR APPLICATIONS, vol.50, pp.66-83, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50
  • Publication Date: 2018
  • Doi Number: 10.1016/j.ffa.2017.11.005
  • Title of Journal : FINITE FIELDS AND THEIR APPLICATIONS
  • Page Numbers: pp.66-83

Abstract

Let K = F-2(k) denote the finite field of 2(k) elements. The Walsh transform of a class of Gold type functions f(x) = Tr-K (x(2a+1) + x(2b+1)), 0 <= a < b at alpha is an element of K is determined in recent results of Lahtonen et al. (2007) [7], Roy (2012) [10] and Cosgun et al. (2016) [2] under some restrictions on k, a, b and a. In this paper, we give explicit evaluation of the Walsh transforms off without any restriction on k, a, b and alpha. Therefore we improve and generalize the related results in literature. Furthermore, we evaluate the Walsh transform of a more general Gold type function f gamma(x) = Tr-K (gamma x(2a+1) + gamma x(2b+1)) 0 <= a < b at alpha is an element of K for any gamma is an element of F-2(k) boolean AND F-2(b-a) without any restriction on k, a, b and alpha. (C) 2017 Elsevier Inc. All rights reserved.