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 |
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Pages (from-to) | 45-59 |
Number of pages | 15 |
Journal | Journal of Combinatorial Designs |
Volume | 23 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Jan 2015 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Algebraic number theory
- Aperiodic autocorrelation
- Barker array
- Three-phase