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|Title:||Optimal odd-length binary Z-complementary pairs||Authors:||Liu, Zilong
Guan, Yong Liang
|Keywords:||DRNTU::Engineering::Computer science and engineering::Information systems||Issue Date:||2014||Source:||Liu, Z., Parampalli, U., & Guan, Y. L. (2014). Optimal odd-length binary Z-complementary pairs. IEEE transactions on information theory, 60(9), 5768-5781.||Series/Report no.:||IEEE transactions on information theory||Abstract:||A pair of sequences is called a Golay complementary pair (GCP) if their aperiodic auto-correlation sums are zero for all out-of-phase time shifts. Existing known binary GCPs only have even-lengths in the form of 2 10 26 (where ; ; are non-negative integers). To fill the gap left by the odd-lengths, we investigate the optimal odd-length binary pairs which display the closest correlation property to that of GCPs. Our criteria of “closeness” is that each pair has the maximum possible zerocorrelation zone (ZCZ) width and minimum possible out-of-zone aperiodic auto-correlation sums. Such optimal pairs are called optimal odd-length binary Z-complementary pairs (OB-ZCP) in this paper. We show that each optimal OB-ZCP has maximum ZCZ width of (N + 1)=2, and minimum out-of-zone aperiodic sum magnitude of 2, where N denotes the sequence length (odd). Systematic constructions of such optimal OP-ZCPs are proposed by insertion and deletion of certain binary GCPs, which settle the 2011 Li-Fan-Tang-Tu open problem positively. The proposed optimal OB-ZCPs may serve as a replacement for GCPs in many engineering applications where odd sequence lengths are preferred. In addition, they give rise to a new family of base-two almost difference families (ADF) which are useful in studying partially balanced incomplete block design (BIBD).||URI:||https://hdl.handle.net/10356/79498
|DOI:||10.1109/TIT.2014.2335731||Rights:||© 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at: [http://dx.doi.org/10.1109/TIT.2014.2335731].||Fulltext Permission:||open||Fulltext Availability:||With Fulltext|
|Appears in Collections:||EEE Journal Articles|
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