Perfect Gaussian Integer Sequences of Arbitrary Composite Length

A composite number can be factored into either N=mp or N=2 n , where p is an odd prime and m, n ≥ 2 are integers. This paper proposes a method for constructing degree-3 and degree-4 perfect Gaussian integer sequences (PGISs) of an arbitrary composite length utilizing an upsampling technique and the...

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Bibliographic Details
Published in:IEEE transactions on information theory 2015-07, Vol.61 (7), p.4107-4115
Main Authors: Chang, H, Li, C, Lee, C, Wang, S, Wu, T
Format: Article
Language:English
Subjects:
Computational complexity
Correlation
Discrete Fourier transforms
Frequency-domain analysis
Gaussian integer
Integer programming
Normal distribution
perfect sequence
periodic auto-correlation function (PACF)
Sampling
Sun
Synchronization
Time-domain analysis
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Summary:A composite number can be factored into either N=mp or N=2 n , where p is an odd prime and m, n ≥ 2 are integers. This paper proposes a method for constructing degree-3 and degree-4 perfect Gaussian integer sequences (PGISs) of an arbitrary composite length utilizing an upsampling technique and the base sequence concept proposed by Hu, Wang, and Li. In constructing the PGISs, the degree of the sequence is defined as the number of distinct nonzero elements within one period of the sequence. This paper commences by constructing degree-3 PGISs of odd prime length, followed by degree-2 PGISs of odd prime length. The proposed method is then extended to the construction of degree-3 and degree-4 PGISs of composite length N=mp. Finally, degree-3 and degree-4 PGISs of length N=4 are built to facilitate the construction of degree-3 and degree-4 PGISs of length N=2 n , where n ≥ 3.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2015.2438828