LAUSR

In analogy to the corresponding measures of pseudorandomness for quaternary sequences introduced by Mauduit and Sárközy (for m-ary sequences) we introduce the well-distribution measure and correlation measure of order k for sequences over $$\mathbb F_4$$F4. Using any fixed bijection from $$\mathbb F_4$$F4 to the set of complex fourth roots of unity, we analyze the relation of these pseudorandomness measures for sequences over $$\mathbb F_4$$F4 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 $$\mathbb F_4$$F4 and vice versa.