  Gaussian random number generators attract a widespread interest due to their
applications in several fields. Important requirements include easy
implementation, tail accuracy, and, finally, a flat spectrum. In this work, we
study the applicability of uniform pseudorandom binary generators in
combination with the Central Limit Theorem to propose an easy to implement,
efficient and flexible algorithm that leverages the properties of the
pseudorandom binary generator used as an input, specially with respect to the
correlation measure of higher order, to guarantee the quality of the generated
samples. Our main result provides a relationship between the pseudorandomness
of the input and the statistical moments of the output. We propose a design
based on the combination of pseudonoise sequences commonly used on wireless
communications with known hardware implementation, which can generate sequences
with guaranteed statistical distribution properties sufficient for many real
life applications and simple machinery. Initial computer simulations on this
construction show promising results in the quality of the output and the
computational resources in terms of required memory and complexity.
