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On the pseudorandomness of quaternary sequences derived from sequences over $$mathbb F_4$$
Authors:Ming Su  Arne Winterhof
Affiliation:1.Department of Computer Science,Nankai University,Tianjin,People’s Republic of China;2.Johann Radon Institute for Computational and Applied Mathematics,Linz,Austria
Abstract: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). 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.
Keywords:
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