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Characterization of p-ary bent functions in terms of strongly regular graphs

Title
Characterization of p-ary bent functions in terms of strongly regular graphs
Authors
Hyun J.Y.Lee Y.
Ewha Authors
이윤진
SCOPUS Author ID
이윤진scopus
Issue Date
2019
Journal Title
IEEE Transactions on Information Theory
ISSN
0018-9448JCR Link
Citation
IEEE Transactions on Information Theory vol. 65, no. 1, pp. 676 - 684
Keywords
(amorphic) association schemep-ary bent functionstrongly regular graph
Publisher
Institute of Electrical and Electronics Engineers Inc.
Indexed
SCIE; SCOPUS WOS scopus
Document Type
Article
Abstract
A p-ary function f in n variables is an l-form if f (tu) = t l f (u) for any nonzero t in Zp and u in Zn p. Let n be a positive even integer, p an odd prime, and l an element of {1, 2, . . . , p-1} provided that l ≠= p-1 if p > 3. Let f be a p-ary bent function in n variables of l -form with f (0) = 0 and gcd(l- 1, p- 1) = 1, and let Hl = {t l : T ϵ Z p}. We denote by G f,l the Cayley graph Cay(Zn p, ∪ϵs-Hl f-1(s)). Our main results are as follows: 1) if there is weakly regular p-ary bent f which is not regular, then l is 2; 2) if l = 2, then f is weakly regular p-ary bent if and only if the Cayley graph G f,l is strongly regular; 3) if l ≠= 2, then f is regular p-ary bent if and only if the Cayley graph G f,l is strongly regular; 4) G f,l can be replaced by Cay(Zn p, f-1(0)\{0}) in 2) and 3); and 5) amorphic association schemes are derived by using 2) and 3). We prove our main results by computing at most four distinct restricted eigenvalues of G f,l . © 1963-2012 IEEE.
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DOI
10.1109/TIT.2018.2843818
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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