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A construction of weakly and non-weakly regular bent functions over the ring of integers modulo
Date
2015-10-01
Author
ÇELİK, Dilek
Özbudak, Ferruh
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This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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Bent functions over the finite fields of an odd characteristic received a lot of attention of late years. In CeAYmelioglu et al. (J Comb Theory Ser A 119:420-429, 2012), CeAYmelioglu and Meidl (Des Codes Cryptogr 66:231-242, 2013), an efficient method of construction of weakly regular and non-weakly regular bent functions defined over a finite field with odd characteristic is presented. In this paper, we give an adaptation of this method to the ring of integers modulo , where p is an odd prime and m is a positive integer. We emphasize that different results than the results of the finite field case are obtained in every application process. First, we give a method that constructs bent functions using plateaued functions by increasing the dimension. Then, in order to give concrete examples, we compute Walsh spectrum of some specific quadratic functions defined over the ring of integers modulo and apply the construction method on these functions. There are notable differences between the cases when m is odd and even. Also, we explain how to determine weakly regular and non-weakly regular bent functions among the bent functions that are constructed by the method.
Subject Keywords
Bent
,
Near-Bent
,
Plateaued Functions
,
Weakly Regular
,
Non-Weakly Regular
,
Finite Rings
,
Walsh Spectrum
URI
https://hdl.handle.net/11511/42695
Journal
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
DOI
https://doi.org/10.1007/s00200-015-0266-3
Collections
Department of Mathematics, Article