Imprimitive symmetric association schemes of classes 5 and 6 arising from ternary non-weakly regular bent functions

Özbudak, Ferruh
Pelen, Rumi Melih
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.


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Let G be a finite group and V be an orthogonal four-dimensional real representation space of G where the action of G is non-free. We give necessary and sufficient conditions for the existence of a G-equivariant vector field on the representation sphere of V in the cases G is the dihedral group, the generalized quaternion group and the semidihedral group in terms of decomposition of V into irreducible representations. In the case G is abelian, where the solution is already known, we give a more elementary so...
Citation Formats
F. Özbudak and R. M. Pelen, “Imprimitive symmetric association schemes of classes 5 and 6 arising from ternary non-weakly regular bent functions,” JOURNAL OF ALGEBRAIC COMBINATORICS, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: