Binary bent functions have a strictly specified number of non-zero values. In the same way, ternary bent functions satisfy certain requirements on the elements of their value vectors. These requirements can be used to specify six classes of ternary bent functions. Classes are mutually related by encoding of function values. Given a basic ternary bent function, other functions in the same class can be constructed by permutation matrices having a block structure similar to that of the factor matrices appearing in the Good-Thomas decomposition of Cooley-Tukey Fast Fourier transform and related algorithms.

This paper describes a method for the efficient computation of the total autocorrelation for large multiple-output Boolean functions over a Shared Binary Decision Diagram (SBDD). The existing methods for computing the total autocorrelation over decision diagrams are restricted to single output functions and in the case of multiple-output functions require repeating the procedure k times where k is the number of outputs. The proposed method permits to perform the computation in a single traversal of SBDD. In that order, compared to standard BDD packages, we modified the way of traversing sub-diagrams in SBDD and introduced an additional memory function kept in the hash table for storing results of the computation of the autocorrelation between two subdiagrams in the SBDD. Due to that, the total amount of computations is reduced which makes the method feasible in practical applications. Experimental results over standard benchmarks confirm the efficiency of the method.