Additive Decomposition of Bent Functions

An additive decomposition of multiple-valued bent functions is studied. It is shown that multiple-valued bent functions may be decomposed with respect to the arithmetic addition, the modulo p addition and the tensor sum of value vectors of p-valued functions. The number of some possible decompositions of bent functions is determined. Examples of additive decomposition of p-valued bent functions for p ∈ {3, 4, 5} are given. It is shown that under structural conditions there are functions which are not bent, but may have close related decompositions.