New complementary sets of length $2^m$ and size 4

Gaofei  Wu; Yuqing  Zhang; Xuefeng  Liu

doi:10.3934/amc.2016043

Article Contents

2016, Volume 10, Issue 4: 825-845. Doi: 10.3934/amc.2016043

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New complementary sets of length $2^m$ and size 4

1.
State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an, 710071
2.
National Computer Network Intrusion Protection Center, UCAS, Beijing 100043

Received: December 31, 2014

Revised: March 31, 2016

Published: October 2016

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Abstract

We construct new complementary sequence sets of size $4$, using a graphical description. We explain how the construction can be seen as a special case of a less explicit array construction by Parker and Riera and, at the same time, a generalization of another construction by the same authors. Some generalizations of the construction are also given, which are not in the construction of Parker and Riera. Lower bounds and upper bounds of the number of sequences in the constructions are analyzed.

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Mathematics Subject Classification: Primary: 94A55, 68P30; Secondary: 05A15.

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