On ternary symmetric bent functions

Abstract

This work was motivated by the fact that in the binary domain there are exactly 4 symmetric bent functions for every even n. A first study in the ternary domain shows very different properties. There are exactly 36 ternary symmetric bent functions of 2 variables, at least 12 ternary symmetric bent functions of 3 variables and at least 36 ternary symmetric bent functions of 4 variables. Furthermore the concept of strong symmetric bent function is introduced. To generate ternary symmetric 2k-place bent functions the tensor sum of two k-place ternary symmetric and the Maiorana Method were analyzed and combined with a set of spectral invariant operations. For n = 3 ternary symmetric bent functions were studied on a class of bent functions in the Reed-Muller domain, and a special adaptation of the tensor sum method was used, obtaining 18 ternary strong symmetric bent functions.