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Designs, Codes and Cryptography
Erschienen in: Designs, Codes and Cryptography 5/2022

05.04.2022

Constructions of two-dimensional Z-complementary array pairs with large ZCZ ratio

verfasst von: Hui Zhang, Cuiling Fan, Sihem Mesnager

Erschienen in: Designs, Codes and Cryptography | Ausgabe 5/2022

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Abstract

Two-dimensional (2-D) Z-complementary array pair (ZCAP) is a pair of 2-D arrays, whose 2-D autocorrelation sum gives zero value at all time shifts in a zone around the (0, 0) time shift, except the (0, 0) time shift. The zone is called a zero correlation zone (ZCZ). 2-D ZCAPs include 2-D Golay complementary array pairs (GCAPs) as special cases, and can be applicable in 2-D synchronization. In this paper, we focus on designing new 2-D ZCAPs by exploring two promising approaches. The first construction of 2-D ZCAPs uses 1-D ZCPs as the initial stage, such that any binary ZCP and q-phase ZCP can produce a q-phase 2-D ZCAP. The second construction of 2-D ZCAPs is based on 2-D generalized Boolean functions (GBFs), and the resulting 2-D ZCAPs can have the largest 2-D ZCZ ratio 6/7, compared with known 2-D ZCAPs but not 2-D GCAPs in the literature. Here the ZCZ ratio is defined as the ratio of the ZCZ size over the array size.
Vorheriger Artikel On Pappus configurations in Hall planes
Nächster Artikel Polycyclic codes associated with trinomials: good codes and open questions
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Metadaten
Titel
Constructions of two-dimensional Z-complementary array pairs with large ZCZ ratio
verfasst von
Hui Zhang
Cuiling Fan
Sihem Mesnager
Publikationsdatum
05.04.2022
Verlag
Springer US
Erschienen in
Designs, Codes and Cryptography / Ausgabe 5/2022
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-022-01035-1

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