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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
- 이윤진
- Issue Date
- 2019
- Journal Title
- IEEE Transactions on Information Theory
- ISSN
- 0018-9448
- Citation
- IEEE Transactions on Information Theory vol. 65, no. 1, pp. 676 - 684
- Keywords
- (amorphic) association scheme; p-ary bent function; strongly regular graph
- Publisher
- Institute of Electrical and Electronics Engineers Inc.
- Indexed
- SCIE; 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.
- DOI
- 10.1109/TIT.2018.2843818
- Appears in Collections:
- 자연과학대학 > 수학전공 > Journal papers
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