Imprimitive symmetric association schemes of classes 5 and 6 arising from ternary non-weakly regular bent functions
JOURNAL OF ALGEBRAIC COMBINATORICS, vol.56, no.3, pp.635-658, 2022 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 56 Issue: 3
- Publication Date: 2022
- Doi Number: 10.1007/s10801-022-01126-1
- Journal Name: JOURNAL OF ALGEBRAIC COMBINATORICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
- Page Numbers: pp.635-658
- Keywords: Non-weakly regular bent, Cayley graph, Translation scheme, Association scheme, Fusion scheme
- Middle East Technical University Affiliated: Yes
Abstract
Let F be a ternary non-weakly regular bent function in GMMF class whose dual F* is bent. We prove that if F satisfies certain conditions, then collecting the pre-image sets of the dual function F* with respect to the subsets B+(F) and B_(F) forms an imprimitive symmetric translation scheme of class 5 (resp. 6) if the dimension is odd (resp. even). Hence, we construct two infinite families of imprimitive symmetric association schemes. Moreover, fusing the first or last three non-trivial relations, we obtain association schemes of classes 3 and 4, respectively.