Distribution of r-patterns in the most significant bit of a maximum length sequence over Z2l

Authors:
Patrick Solé;Dmitrii Zinoviev
Affiliations:
CNRS-I3S, ESSI, Sophia Antipolis, France;Institute for Problems of Information Transmission, Russian Academy of Sciences, Moscow, Russia
Venue:
SETA'04 Proceedings of the Third international conference on Sequences and Their Applications
Year:
2004

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Abstract

The number of subwords of length r and of given value within a period of a sequence in the title is shown to be close to equidistribution. Important tools in the proof are a higher order correlation and Galois ring character sum estimates.