The density of ternary barker sequences

Authors:
Tomas Boothby
Affiliations:
Simon Fraser University, Burnaby, BC, Canada
Venue:
SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
Year:
2012

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Abstract

Ternary Barker sequences are sequences whose elements are in -1,0,1 for which every aperiodic offset autocorrelation has magnitude at most 1. Despite promising properties, they have received little attention from both the signals and mathematics communities. In this paper, we demonstrate the existence of ternary Barker sequences to answer a question of Millar. We enumerate ternary Barker sequences of length up to 44 and summarize some features of these sequences. Of primary interest is the density, or proportion of nonzero entries in a sequence. We also briefly examine the relation between density and merit factor.