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


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

EUROPEAN JOURNAL OF COMBINATORICS, cilt.80, ss.71-81, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 80
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1016/j.ejc.2018.02.025
  • Dergi Adı: EUROPEAN JOURNAL OF COMBINATORICS
  • Sayfa Sayıları: ss.71-81

Özet

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.