A Note on Hall’s Sextic Residue Sequence: Correlation Measure of Order [Formula Omitted] and Related Measures of Pseudorandomness

It is known that Hall’s sextic residue sequence has some desirable features of pseudorandomness: an ideal two-level autocorrelation and linear complexity of the order of magnitude of its period [Formula Omitted]. Here we study its correlation measure of order [Formula Omitted] and show that it is, u...

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Published inIEEE transactions on information theory Vol. 66; no. 3; p. 1944
Main Authors Aly, Hassan, Winterhof, Arne
Format Journal Article
LanguageEnglish
Published New York The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 01.03.2020
Subjects
Complexity
Correlation analysis
Lower bounds
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Abstract It is known that Hall’s sextic residue sequence has some desirable features of pseudorandomness: an ideal two-level autocorrelation and linear complexity of the order of magnitude of its period [Formula Omitted]. Here we study its correlation measure of order [Formula Omitted] and show that it is, up to a constant depending on [Formula Omitted] and some logarithmic factor, of order of magnitude [Formula Omitted], which is close to the expected value for a random sequence of length [Formula Omitted]. Moreover, we derive from this bound a lower bound on the [Formula Omitted]th maximum order complexity of order of magnitude [Formula Omitted], which is the expected order of magnitude for a random sequence of length [Formula Omitted].
AbstractList It is known that Hall’s sextic residue sequence has some desirable features of pseudorandomness: an ideal two-level autocorrelation and linear complexity of the order of magnitude of its period [Formula Omitted]. Here we study its correlation measure of order [Formula Omitted] and show that it is, up to a constant depending on [Formula Omitted] and some logarithmic factor, of order of magnitude [Formula Omitted], which is close to the expected value for a random sequence of length [Formula Omitted]. Moreover, we derive from this bound a lower bound on the [Formula Omitted]th maximum order complexity of order of magnitude [Formula Omitted], which is the expected order of magnitude for a random sequence of length [Formula Omitted].
Author Winterhof, Arne
Aly, Hassan
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SubjectTerms Complexity
Correlation analysis
Lower bounds
Title A Note on Hall’s Sextic Residue Sequence: Correlation Measure of Order [Formula Omitted] and Related Measures of Pseudorandomness
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