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IMA International Conference on Cryptography and Coding

IMACC 2011: Cryptography and Coding pp 41–60Cite as

Generalised Complementary Arrays

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7089))

Abstract

We present a generalised setting for the construction of complementary array pairs and its proof, using a unitary matrix notation. When the unitaries comprise multivariate polynomials in complex space, we show that four definitions of conjugation imply four types of complementary pair - types I, II, III, and IV. We provide a construction for complementary pairs of types I, II, and III over {1, − 1}, and further specialize to a construction for all known 2 ×2 ×…×2 complementary array pairs of types I, II, and III over {1, − 1}. We present a construction for type-IV complementary array pairs, and call them Rayleigh quotient pairs. We then generalise to complementary array sets, provide a construction for complementary sets of types I, II, and III over {1, − 1}, further specialize to a construction for all known 2 ×2 ×…×2 complementary array sets of types I, II, and III over {1, − 1}, and derive closed-form Boolean formulas for these cases.

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Author information

Authors and Affiliations

  1. The Selmer Center, Department of Informatics, University of Bergen, PB 7800, N-5020, Bergen, Norway

    Matthew G. Parker

  2. Høgskolen i Bergen, Bergen, Norway

    Constanza Riera

Authors
  1. Matthew G. Parker
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  2. Constanza Riera
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Editor information

Editors and Affiliations

  1. Hewlett-Packard Laboratories, UK

    Liqun Chen

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© 2011 Springer-Verlag Berlin Heidelberg

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Parker, M.G., Riera, C. (2011). Generalised Complementary Arrays. In: Chen, L. (eds) Cryptography and Coding. IMACC 2011. Lecture Notes in Computer Science, vol 7089. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25516-8_4

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  • DOI: https://doi.org/10.1007/978-3-642-25516-8_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25515-1

  • Online ISBN: 978-3-642-25516-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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