Negabent functions were introduced as a generalization of bent functions,
which have applications in coding theory and cryptography. In this paper, we
have extended the notion of negabent functions to the functions defined from
Zqnβ to Z2qβ (2q-negabent), where qβ₯2 is a
positive integer and Zqβ is the ring of integers modulo q. For
this, a new unitary transform (the nega-Hadamard transform) is introduced in
the current set up, and some of its properties are discussed. Some results
related to 2q-negabent functions are presented. We present two constructions
of 2q-negabent functions. In the first construction, 2q-negabent functions
on n variables are constructed when q is an even positive integer. In the
second construction, 2q-negabent functions on two variables are constructed
for arbitrary positive integer qβ₯2. Some examples of 2q-negabent
functions for different values of q and n are also presented