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자연과학대학
수학전공
Journal papers
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Characterization of p-ary functions in terms of association schemes and its applications
Title
Characterization of p-ary functions in terms of association schemes and its applications
Authors
Wu Y.
;
Hyun J.Y.
;
Lee Y.
Ewha Authors
이윤진
SCOPUS Author ID
이윤진
Issue Date
2022
Journal Title
Journal of Combinatorial Theory. Series A
ISSN
0097-3165
Citation
Journal of Combinatorial Theory. Series A vol. 187
Keywords
Association scheme
;
Few-weight linear code
;
p-ary function
;
Walsh transform
Publisher
Academic Press Inc.
Indexed
SCIE; SCOPUS
Document Type
Article
Abstract
We obtain an explicit criterion for p-ary functions to produce association schemes in terms of their Walsh spectrum. Employing this characterization, we explicitly find a correlation between p-ary bent functions and association schemes; to be more exact, we prove that a p-ary bent function induces a p-class association scheme if and only if the function is weakly regular. As applications of our main criterion, we construct many infinite families of few-class association schemes arising from p-ary functions. Furthermore, we present four classes of p-ary two-weight linear codes, which are constructed from the association schemes produced in this paper. © 2021 Elsevier Inc.
DOI
10.1016/j.jcta.2021.105576
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