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


ÖZBUDAK F. , Pelen R. M.

JOURNAL OF ALGEBRAIC COMBINATORICS, 2022 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1007/s10801-022-01126-1
  • Title of Journal : JOURNAL OF ALGEBRAIC COMBINATORICS
  • Keywords: Non-weakly regular bent, Cayley graph, Translation scheme, Association scheme, Fusion scheme

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.