Ramanujan graphs and expander families constructed from p-ary bent functions
- 주제(키워드) (amorphic)association scheme , Expanders , p-ary bent function , Ramanujan graph
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 Springer
- 발행년도 2020
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000166057
- 본문언어 영어
- Published As http://dx.doi.org/10.1007/s10623-019-00692-z
초록/요약
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.
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