On q-ary plateaued functions over F-q and their explicit characterizations

Mesnager S., ÖZBUDAK F., Sinak A., Cohen G.

EUROPEAN JOURNAL OF COMBINATORICS, vol.80, pp.71-81, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 80
  • Publication Date: 2019
  • Doi Number: 10.1016/j.ejc.2018.02.025
  • Journal Name: EUROPEAN JOURNAL OF COMBINATORICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.71-81
  • Middle East Technical University Affiliated: Yes

Abstract

Plateaued and bent functions play a significant role in cryptography, sequence theory, coding theory and combinatorics. In 1997, Coulter and Matthews redefined bent functions over any finite field F-q where q is a prime power, and established their properties. The objective of this work is to redefine the notion of plateaued functions over F-q, and to present several explicit characterizations of those functions. We first give, over F-q, the notion of q-ary plateaued functions, which relies on the concept of the Walsh-Hadamard transform in terms of canonical additive character of F-q. We then give a concrete example of q-ary plateaued function, that is not vectorial p-ary plateaued function. This suggests that the study of plateaued-ness is also significant for q-ary functions over Fq. We finally characterize q-ary plateaued functions in terms of derivatives, Walsh power moments and autocorrelation functions. (C) 2018 Elsevier Ltd. All rights reserved.