Three-phase Barker arrays

Jason P. Bell; Jonathan Jedwab; Mahdad Khatirinejad; Kai Uwe Schmidt

doi:10.1002/jcd.21377

Three-phase Barker arrays

Jason P. Bell^*, Jonathan Jedwab, Mahdad Khatirinejad , Kai Uwe Schmidt

^*Corresponding author for this work

Department of Communications and Networking

Research output: Contribution to journal › Article › Scientific › peer-review

1 Citation (Scopus)

Abstract

A 3-phase Barker array is a matrix of third roots of unity for which all out-of-phase aperiodic autocorrelations have magnitude 0 or 1. The only known truly two-dimensional 3-phase Barker arrays have size 2 × 2 or 3 × 3. We use a mixture of combinatorial arguments and algebraic number theory to establish severe restrictions on the size of a 3-phase Barker array when at least one of its dimensions is divisible by 3. In particular, there exists a doubleexponentially growing arithmetic function T such that no 3-phase Barker array of size s × t with 3

Original language	English
Pages (from-to)	45-59
Number of pages	15
Journal	Journal of Combinatorial Designs
Volume	23
Issue number	2
DOIs	https://doi.org/10.1002/jcd.21377
Publication status	Published - 1 Jan 2015
MoE publication type	A1 Journal article-refereed

Keywords

Algebraic number theory
Aperiodic autocorrelation
Barker array
Three-phase

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10.1002/jcd.21377

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