Mesnager, SihemOzbudak, FerruhSinak, AhmetCohen, Gerard2024-02-232024-02-2320190195-66981095-9971https://doi.org/10.1016/j.ejc.2018.02.025https://hdl.handle.net/20.500.12452/11830Plateaued 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.eninfo:eu-repo/semantics/openAccess[Keyword Not Available]Article8071812-s2.0-85042490121Q1WOS:000474675900009Q210.1016/j.ejc.2018.02.025