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Designs, Codes and Cryptography

, Volume 80, Issue 2, pp 283–294 | Cite as

A construction and decomposition of orthogonal arrays with non-prime-power numbers of symbols on the complement of a Baer subplane

  • Kohei YamadaEmail author
  • Nobuko Miyamoto
Article
  • 160 Downloads

Abstract

Fuji-Hara and Kamimura (Util Math 43:65–70, 1993) outlined a method for constructing orthogonal arrays of strength 2 on the complement of a Baer subplane, with \(q(q-1)\) symbols for a prime power \(q\). In this paper, we demonstrate that these orthogonal arrays can be decomposed into other orthogonal arrays of strength 2, with the same numbers of constraints and symbols but with smaller sizes and indices. In our construction, each orthogonal array of the decomposition can be obtained as an orbit of the point-set of a Baer subplane, under the action of a certain projective linear group. Furthermore, for \(q \equiv 2 \pmod 3\) and \(q > 2\), a series of the new orthogonal arrays cannot be obtained by Bush’s direct product construction, which is a classical method for constructing orthogonal arrays with non-prime-power numbers of symbols.

Keywords

Baer subplane Decomposition of a design Group divisible design Orthogonal array Transversal design Singer Baer partition 

Mathematics Subject Classification

51E20 05B15 05B05 

Notes

Acknowledgments

The authors would like to thank Prof. Ryoh Fuji-Hara and Prof. Masakazu Jimbo for their valuable comments, and also thank the anonymous referees for their careful reading and constructive suggestions.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Information ScienceNagoya UniversityNagoya-shiJapan
  2. 2.Department of Information SciencesTokyo University of ScienceNoda-shiJapan

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