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

Date

2019-08-01

Author

Mesnager, Sihem
Özbudak, Ferruh
Sinak, Ahmet
Cohen, Gerard

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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.

Subject Keywords

Discrete Mathematics and Combinatorics

URI

https://hdl.handle.net/11511/43283

Journal

EUROPEAN JOURNAL OF COMBINATORICS

DOI

https://doi.org/10.1016/j.ejc.2018.02.025

Collections

Department of Mathematics, Article

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Citation Formats

S. Mesnager, F. Özbudak, A. Sinak, and G. Cohen, “On q-ary plateaued functions over F-q and their explicit characterizations,” EUROPEAN JOURNAL OF COMBINATORICS, pp. 71–81, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/43283.