A generating matrix method for constructing Hermite-Gaussian-like number-theoretic transform eigenvectors

In this paper, we present a method based on generating matrices for constructing number-theoretic transform (NTT) eigenvectors. We provide a specific generating matrix and, using it, we demonstrate how to construct an orthogonal basis of Hermite-Gaussian-like NTT eigenvectors, which can be used to define a fractional number-theoretic transform (FrNTT). We discuss the main aspects of the referred eigenbasis, present an example and suggest a potential application for the corresponding FrNTT.