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Ramanujan graphs and expander families constructed from p-ary bent functions

Title
Ramanujan graphs and expander families constructed from p-ary bent functions
Authors
Hyun J.Y.Lee J.Lee Y.
Ewha Authors
이윤진
SCOPUS Author ID
이윤진scopus
Issue Date
2020
Journal Title
Designs, Codes, and Cryptography
ISSN
0925-1022JCR Link
Citation
Designs, Codes, and Cryptography vol. 88, no. 2, pp. 453 - 470
Keywords
(amorphic)association schemeExpandersp-ary bent functionRamanujan graph
Publisher
Springer
Indexed
SCI; SCIE; SCOPUS scopus
Document Type
Article
Abstract
We present a method for constructing an infinite family of non-bipartite Ramanujan graphs. We mainly employ p-ary bent functions of (p- 1) -form for this construction, where p is a prime number. Our result leads to construction of infinite families of expander graphs; this is due to the fact that Ramanujan graphs play as base expanders for constructing further expanders. For our construction we directly compute the eigenvalues of the Ramanujan graphs arsing from p-ary bent functions. Furthermore, we establish a criterion on the regularity of p-ary bent functions in m variables of (p- 1) -form when m is even. Finally, using weakly regular p-ary bent functions of ℓ-form, we find (amorphic) association schemes in a constructive way; this resolves the open case that ℓ= p- 1 for p> 2 for finding (amorphic) association schemes. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.
DOI
10.1007/s10623-019-00692-z
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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