On the pseudorandomness of quaternary sequences derived from sequences over $$\mathbb F_4$$ F 4

Abstract

In analogy to the corresponding measures of pseudorandomness for quaternary sequences introduced by Mauduit and Sarkozy (for m-ary sequences) we introduce the well-distribution measure and correlation measure of order k for sequences over \(\mathbb F_4\). Using any fixed bijection from \(\mathbb F_4\) to the set of complex fourth roots of unity, we analyze the relation of these pseudorandomness measures for sequences over \(\mathbb F_4\) and for the corresponding quaternary sequences. More precisely, we show that they differ only by a multiplicative constant (depending only on k). We also apply the results for deriving new quaternary pseudorandom sequences from pseudorandom sequences over \(\mathbb F_4\) and vice versa.