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Switching for 2-designs

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Abstract

In this paper, we introduce a switching for 2-designs, which defines a type of trade. We illustrate this method by applying it to some symmetric (64, 28, 12) designs, showing that the switching introduced in this paper in some cases can be applied directly to orbit matrices. In that way we obtain six new symmetric (64, 28, 12) designs. Further, we show that this type of switching (of trades) can be applied to any symmetric design related to a Bush-type Hadamard matrix and construct symmetric designs with parameters (36, 15, 6) leading to new Bush-type Hadamard matrices of order 36, and symmetric (100, 45, 20) designs yielding Bush-type Hadamard matrices of order 100.

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Acknowledgements

The authors thank the anonymous referees for helpful comments that improved the presentation of the paper.

Funding

This work has been fully supported by Croatian Science Foundation under the projects 6732 and 5713.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Rijeka, Radmile Matejčić 2, 51000, Rijeka, Croatia

    Dean Crnković & Andrea Švob

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  1. Dean Crnković
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  2. Andrea Švob
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Correspondence to Andrea Švob.

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Communicated by V. D. Tonchev.

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Crnković, D., Švob, A. Switching for 2-designs. Des. Codes Cryptogr. 90, 1585–1593 (2022). https://doi.org/10.1007/s10623-022-01059-7

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