# American Institute of Mathematical Sciences

May  2017, 11(2): 367-371. doi: 10.3934/amc.2017030

## A multi-dimensional block-circulant perfect array construction

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

Received  February 2016 Revised  March 2016 Published  May 2017

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).

Citation: Samuel T. Blake, Andrew Z. Tirkel. A multi-dimensional block-circulant perfect array construction. Advances in Mathematics of Communications, 2017, 11 (2) : 367-371. doi: 10.3934/amc.2017030
##### References:
 [1] 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. [2] W. H. Mow, A Study of Correlation of Sequences, Ph. D thesis, The Chinese University of Hong Kong, 1993.

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##### References:
 [1] 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. [2] W. H. Mow, A Study of Correlation of Sequences, Ph. D thesis, The Chinese University of Hong Kong, 1993.
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