New Correlations of m-sequences over the finite field $\mathbb{F}_{4}$ compatible with a new bijection to $\mathbb{Z}_{4}$

In this paper we obtain a new method to compute the correlation values of two arbitrary sequences defined by a mapping from
$\mathbb{F}_{4^{n}}$
to
$\mathbb{F}_{4}$
. We apply this method to demon-strate that the usual nonbinary maximal length sequences have almost ideal correlation under the canonical complex correlation definition and investigate some decimations giving good cross correlation.