A multi-dimensional block-circulant perfect array construction

Samuel T. Blake; Andrew Z. Tirkel

doi:10.3934/amc.2017030

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2017, Volume 11, Issue 2: 367-371. Doi: 10.3934/amc.2017030

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A multi-dimensional block-circulant perfect array construction

Samuel T. Blake and
Andrew Z. Tirkel

School of Mathematical Sciences, Monash University, Building 20, Clayton Campus, Victoria, Australia 3800

Received: January 31, 2016

Revised: February 29, 2016

Published: September 2017

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Abstract

We present an N-dimensional generalisation of the two-dimensional block-circulant perfect array construction by Blake et al. As in Blake et al, the families of N-dimensional arrays possess pairwise good zero correlation zone (ZCZ) cross-correlation. Both constructions use a perfect autocorrelation sequence with the array orthogonality property (AOP).

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Mathematics Subject Classification: 05E05, 05E10, 05E15, 05E18, 05E30, 05E40, 05E45.

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References

	S. Blake , T. E. Hall and A. Z. Tirkel , Arrays over roots of unity with perfect autocorrelation and good ZCZ cross-correlation, Adv. Math. Commun., 7 (2013) , 231-242. doi: 10.3934/amc.2013.7.231.
	W. H. Mow, A Study of Correlation of Sequences, Ph. D thesis, The Chinese University of Hong Kong, 1993.