View : 729 Download: 0
CHARACTERIZATION OF CERTAIN TYPES OF r-PLATEAUED FUNCTIONS
- Title
- CHARACTERIZATION OF CERTAIN TYPES OF r-PLATEAUED FUNCTIONS
- Authors
- Hyun, Jong Yoon; Lee, Jungyun; Lee, Yoonjin
- Ewha Authors
- 이윤진
- SCOPUS Author ID
- 이윤진
- Issue Date
- 2018
- Journal Title
- JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
- ISSN
- 0304-9914
2234-3008
- Citation
- JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY vol. 55, no. 6, pp. 1469 - 1483
- Keywords
- plateaued function; Bent function; cryptographic function
- Publisher
- KOREAN MATHEMATICAL SOC
- Indexed
- SCIE; SCOPUS; KCI
- Document Type
- Article
- Abstract
- We study a subclass of p-ary functions in n variables, denoted by A(n), which is a collection of p-ary functions in n variables satisfying a certain condition on the exponents of its monomial terms. Firstly, we completely classify all p-ary (n - 1)-plateaued functions in n variables by proving that every (n - 1)-plateaued function should be contained in A(n). Secondly, we prove that if f is a p-ary r-plateaued function contained in A(n) with deg f > 1+n-r/4(p - 1), then the highest degree term of f is only a single term. Furthermore, we prove that there is no p-ary r-plateaued function in A(n) with maximum degree (p - 1)n-r/2+1. As application, we partially classify all (n - 2)-plateaued functions in A(n) when p = 3, 5, and 7, and p-ary bent functions in A(2) are completely classified for the cases p = 3 and 5.
- DOI
- 10.4134/JKMS.j170763
- Appears in Collections:
- 자연과학대학 > 수학전공 > Journal papers
- Files in This Item:
There are no files associated with this item.
- Export
- RIS (EndNote)
- XLS (Excel)
- XML