The Density of Ternary Barker Sequences
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.
KeywordsNonzero Entry Binary Sequence FPGA Implementation Merit Factor Ternary Sequence
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