Constructing Generalized Bent Functions from Trace Forms of Galois Rings

Quaternary constant-amplitude codes (codes over \({\mathbb Z}_4\)) of length \(2^m\) exist for every positive integer \(m\), and every codeword of such a code corresponds to a function from the binary \(m\)-tuples to \({\mathbb Z}_4\) having the bent property, called a generalized bent function. In this chapter, we extend previous constructions and propose a general approach which can lead to more generalized bent functions.