On [formula omitted]-ary plateaued functions over [formula omitted] and their explicit characterizations.

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 F q. We finally characterize q -ary plateaued functions in terms of derivatives, Walsh power moments and autocorrelation functions. [ABSTRACT FROM AUTHOR]