Designs, Codes and Cryptography

, Volume 80, Issue 2, pp 283–294

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

• Nobuko Miyamoto
Article

## 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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