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

2022-04-01
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.
JOURNAL OF ALGEBRAIC COMBINATORICS

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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: https://hdl.handle.net/11511/97220.