New constructions of quaternary bent functions

In this paper, a new construction of quaternary bent functions from quaternary quadratic forms over Galois rings of characteristic 4 is proposed. Based on this construction, several new classes of quaternary bent functions are obtained, and as a consequence, several new classes of quadratic binary bent and semi-bent functions in polynomial forms are derived. This work generalizes the recent work of N. Li, X. Tang and T. Helleseth.