On the pseudorandomness of quaternary sequences derived from sequences over $$mathbb F_4$$ |
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Authors: | Ming Su Arne Winterhof |
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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 |
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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. |
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