On the pseudorandomness of quaternary sequences derived from sequences over

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 . Using any fixed bijection from to the set of complex fourth roots of unity, we analyze the relation of these pseudorandomness measures for sequences over 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 and vice versa.