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

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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.

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Acknowledgements

The authors extend thanks to the Associate Editor and the anonymous reviewers for their valuable comments and suggestions, which improved the quality and presentation of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, Dumlupınar Bulvarı No. 1, 06800, Ankara, Turkey

    Ferruh Özbudak

  2. Department of Mathematics, Erzurum Technical University, Yakutiye, Erzurum, Turkey

    Rumi Melih Pelen

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  1. Ferruh Özbudak
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  2. Rumi Melih Pelen
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Correspondence to Ferruh Özbudak.

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Özbudak, F., Pelen, R.M. Imprimitive symmetric association schemes of classes 5 and 6 arising from ternary non-weakly regular bent functions. J Algebr Comb 56, 635–658 (2022). https://doi.org/10.1007/s10801-022-01126-1

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