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Unbiased orthogonal designs

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Abstract

The notion of unbiased orthogonal designs is introduced as a generalization of unbiased Hadamard matrices, unbiased weighing matrices and quasi-unbiased weighing matrices. We provide upper bounds and several methods of construction for mutually unbiased orthogonal designs. As an application, mutually quasi-unbiased weighing matrices for various parameters are obtained.

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Acknowledgements

Hadi Kharaghani is supported by an NSERC Discovery Grant. Sho Suda is supported by JSPS KAKENHI Grant Number 15K21075. The authors wish to thank Darcy Best for showing the validity of Theorem 5.2 for \(t=1\) by computer computation, and Akihiro Munemasa and Pritta Etriana Putri for pointing our some errors, and the referees for their invaluable comments.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, AB, T1K 3M4, Canada

    Hadi Kharaghani

  2. Department of Mathematics Education, Aichi University of Education, 1 Hirosawa, Igaya-cho, Kariya, Aichi, 448-8542, Japan

    Sho Suda

Authors
  1. Hadi Kharaghani
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  2. Sho Suda
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Correspondence to Hadi Kharaghani.

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Communicated by J. H. Koolen.

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Kharaghani, H., Suda, S. Unbiased orthogonal designs. Des. Codes Cryptogr. 86, 1573–1588 (2018). https://doi.org/10.1007/s10623-017-0414-9

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  • DOI: https://doi.org/10.1007/s10623-017-0414-9

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