Open AccessArrays over roots of unity with perfect autocorrelation and good ZCZ cross-correlation
Author(s) -
Samuel T. Blake,
T. E. Hall,
Andrew Z. Tirkel
Publication year - 2013
Publication title -
advances in mathematics of communications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.601
H-Index - 26
eISSN - 1930-5346
pISSN - 1930-5338
DOI - 10.3934/amc.2013.7.231
Subject(s) - mathematics , orthogonality , autocorrelation , root of unity , circulant matrix , block (permutation group theory) , combinatorics , pairwise comparison , zero (linguistics) , exponential function , complementary sequences , sequence (biology) , discrete mathematics , mathematical analysis , geometry , statistics , linguistics , physics , philosophy , quantum mechanics , biology , quantum , genetics
We present a new construction for two-dimensional, perfect autocorrelation arrays over roots of unity. These perfect arrays are constructed from a block of perfect column sequences. Other blocks are constructed from the first block, to generate a block-circulant structure. The columns are then multiplied by a perfect sequence over roots of unity, which, when folded into an array commensurate with our block width has the array orthogonality property. The size of the arrays is commensurate with the length of the underlying perfect sequences. For a given size we can construct an exponential number of inequivalent perfect arrays. For each perfect array we construct a family of arrays whose pairwise cross-correlation values are almost all zero (large zero correlation zones (ZCZ)). We present experimental evidence that this construction for perfect arrays can be generalized to higher dimensions.
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