A new class of negabent functions
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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 ℤ_q^n to ℤ_2q (2q-negabent), where q ≥ 2 is a positive integer and ℤ_q 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 q ≥ 2. Some examples of 2q-negabent functions for different values of q and n are also presented.
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