Abstract
In this paper, using group actions, we introduce a new method for constructing partial geometric designs (sometimes referred to as \(1\frac{1}{2}\)-designs). Using this new method, we construct several infinite families of partial geometric designs by investigating the actions of various linear groups of degree two on certain subsets of \({\mathbb {F}}_{q}^{2}\). Moreover, by computing the stabilizers of such subsets in various linear groups of degree two, we are also able to construct a new infinite family of balanced incomplete block designs.
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The authors are very grateful to the two anonymous reviewers for all of their detailed comments that greatly improved the quality and the presentation of this paper.
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Communicated by Q. Xiang.
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The authors were supported by the National Science Foundation of China under Grant No. 61672015.
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Michel, J., Wang, Q. Partial geometric designs from group actions. Des. Codes Cryptogr. 87, 2655–2670 (2019). https://doi.org/10.1007/s10623-019-00644-7
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DOI: https://doi.org/10.1007/s10623-019-00644-7