On o-Equivalence of Niho Bent Functions

As observed recently by the second author and S. Mesnager, the projective equivalence of o-polynomials defines, for Niho bent functions, an equivalence relation called o-equivalence. These authors also observe that, in general, the two o-equivalent Niho bent functions defined from an o-polynomial F and its inverse F-1 are EA-inequivalent. In this paper we continue the study of o-equivalence. We study a group of order 24 of transformations preserving o-polynomials which has been studied by Cherowitzo 25 years ago. We point out that three of the transformations he included in the group are not correct. We also deduce two more transformations preserving o-equivalence but providing potentially EA-inequivalent bent functions. We exhibit examples of infinite classes of o-polynomials for which at least three EA-inequivalent Niho bent functions can be derived.