  An efficient algorithm for computing the terms appearing in the Generalised
Kolmogorov Equation (GKE) written for the indefinite plane channel flow is
presented. The algorithm, which features three distinct strategies for parallel
computing, is designed such that CPU and memory requirements are kept to a
minimum, so that high-Re wall-bounded flows can be afforded. Computational
efficiency is mainly achieved by leveraging the Parseval's theorem for the two
homogeneous directions available in the plane channel geometry. A speedup of
3-4 orders of magnitude, depending on the problem size, is reported in
comparison to a key implementation used in the literature. Validation of the
code is demonstrated by computing the residual of the GKE, and example results
are presented for channel flows at Re_{\tau}=200 and Re_{\tau}=1000, where for
the first time they are observed in the whole four-dimensional domain. It is
shown that the space and scale properties of the scale-energy fluxes change for
increasing values of the Reynolds number. Among all scale-energy fluxes, the
wall-normal flux is found to show the richest behaviour for increasing
streamwise scales.
