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Explicit criterions for p-ary functions being non-bent

Title
Explicit criterions for p-ary functions being non-bent
Authors
Hyun, Jong YoonLee, Yoonjin
Ewha Authors
이윤진현종윤
SCOPUS Author ID
이윤진scopus; 현종윤scopus
Issue Date
2016
Journal Title
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN
0022-247XJCR Link1096-0813JCR Link
Citation
vol. 433, no. 2, pp. 1177 - 1189
Keywords
Boolean functionp-ary functionp-ary bent functionWeakly regular p-ary bent function
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
There has been only limited information on the existence of p-ary bent functions. Recently there has been a result by the authors on finding necessary conditions for the existence of regular p-ary bent functions (from Z(p)(n); to Z(p)), where p is a prime. The general case of p-ary bent functions is, however, an open question for finding necessary conditions for their existence. In this paper we complete this open case. We state our main result in more detail. We find an explicit family of non-bent functions. We also show that there is no p-ary bent function f in n variables with w(Mf) > n/2 n is even (w(Mf) > n+3/2 if n is odd, respectively), and for a given nonnegative integer k there is no p-ary bent function f in n variables with w(Mf) = n/2 - k (w(Mf) = n+3/2 - k, respectively) for an even n >= N-p,N-k (for an odd n >= N-p,N-k, respectively), where Np,k is some positive integer which is explicitly determined and w(M1) is some explicit value related to the power of each monomial of f. We point out that if f is not a p-ary bent function in n variables and g is any p-ary function in n variables such that L(G(f)) = G(g) for some CCZ-transformation of f, then g cannot be bent either. This shows that our result produces a larger family of non-bent functions. (C) 2015 Elsevier Inc. All rights reserved.
DOI
10.1016/j.jmaa.2015.08.045
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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