Cryptography and Communications

, Volume 6, Issue 1, pp 3–25

A complementary construction using mutually unbiased bases


DOI: 10.1007/s12095-013-0095-9

Cite this article as:
Wu, G. & Parker, M.G. Cryptogr. Commun. (2014) 6: 3. doi:10.1007/s12095-013-0095-9


We propose a construction for complementary sets of arrays that exploits a set of mutually-unbiased bases (a MUB). In particular we present, in detail, the construction for complementary pairs that is seeded by a MUB of dimension 2, where we enumerate the arrays and the corresponding set of complementary sequences obtained from the arrays by projection. We also sketch an algorithm to uniquely generate these sequences. The pairwise squared inner-product of members of the sequence set is shown to be \(\frac {1}{2}\). Moreover, a subset of the set can be viewed as a codebook that asymptotically achieves \(\sqrt {\frac {3}{2}}\) times the Welch bound.


Mutually unbiased bases Complementary sequences PAPR Codebooks OFDM 

Mathematics Subject Classifications

42C10 55T99 15B10 

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.State Key Laboratory of Integrated Service NetworksXidian UniversityXi’anChina
  2. 2.Department of InformaticsUniversity of BergenBergenNorway

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