Several Types of Sequences with Optimal Autocorrelation Properties

Fanxin ZENG  Xiaoping ZENG  Xiangyong ZENG  Zhenyu ZHANG  Guixin XUAN  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.1   pp.367-372
Publication Date: 2013/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.367
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Information Theory
binary sequences,  quaternary sequences,  perfect QPSK+ sequences,  multilevel perfect sequences,  

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This letter presents a framework, including two constructions, for yielding several types of sequences with optimal autocorrelation properties. Only by simply choosing proper coefficients in constructions and optimal known sequences, two constructions transform the chosen sequences into optimally required ones with two or four times periods as long as the original sequences', respectively. These two constructions result in binary and quaternary sequences with optimal autocorrelation values (OAVs), perfect QPSK+ sequences, and multilevel perfect sequences, depending on choices of the known sequences employed. In addition, Construction 2 is a generalization of Construction B in [5] so that the number of distinct sequences from the former is larger than the one from the latter.