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A Class of Ternary Sequence Sets with a ZeroCorrelation Zone for Periodic, Aperiodic, and Odd Correlation Functions
Takafumi HAYASHI
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E86A
No.7
pp.18501857 Publication Date: 2003/07/01
Online ISSN:
DOI:
Print ISSN: 09168508 Type of Manuscript: PAPER Category: Spread Spectrum Technologies and Applications Keyword: ternary sequence, finitelength sequence, zerocorrelation zone, aperiodic correlation function, odd correlation function,
Full Text: PDF>>
Summary:
The present paper introduces a new approach to the construction of a class of ternary sequences having a zerocorrelation zone. The crosscorrelation function of each pair of the proposed sequences is zero for phase shifts within the zerocorrelation zone, and the autocorrelation function of each proposed sequence is zero for phase shifts within the zerocorrelation zone, except for zeroshift. The proposed sequence set has a zerocorrelation zone for periodic, aperiodic, and odd correlation functions. As such, the proposed sequence can be used as a finitelength sequence with a zerocorrelation zone. A set of the proposed sequences can be constructed for any set of Hadamard sequences of length n. The constructed sequence set consists of 2n ternary sequences, and the length of each sequence is (n+1)2^{m+2} for a nonnegative integer m. The periodic correlation function, the aperiodic correlation function, and the odd correlation function of the proposed sequences have a zerocorrelation zone from (2^{m+1}1) to (2^{m+1}1). The member size of the proposed sequence set is of the theoretical upper bound of the member size of a sequence having a zerocorrelation zone. The ratio of the number of nonzero elements to the the sequence length of the proposed sequence is also .

