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.
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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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Communicated by T. Penttila.
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Yamada, K., Miyamoto, N. A construction and decomposition of orthogonal arrays with non-prime-power numbers of symbols on the complement of a Baer subplane. Des. Codes Cryptogr. 80, 283–294 (2016). https://doi.org/10.1007/s10623-015-0086-2
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DOI: https://doi.org/10.1007/s10623-015-0086-2
Keywords
- Baer subplane
- Decomposition of a design
- Group divisible design
- Orthogonal array
- Transversal design
- Singer Baer partition