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A recursive construction for simple t-designs using resolutions

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Abstract

This work presents a recursive construction for simple t-designs using resolutions of the ingredient designs. The result extends a construction of t-designs in our recent paper van Trung (Des Codes Cryptogr 83:493–502, 2017). Essentially, the method in van Trung (Des Codes Cryptogr 83:493–502, 2017) describes the blocks of a constructed design as a collection of block unions from a number of appropriate pairs of disjoint ingredient designs. Now, if some pairs of these ingredient t-designs have both suitable s-resolutions, then we can define a distance mapping on their resolution classes. Using this mapping enables us to have more possibilities for forming blocks from those pairs. The method makes it possible for constructing many new simple t-designs. We give some application results of the new construction.

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Acknowledgements

The author would like to thank the anonymous reviewers for their careful reading of the manuscript and their helpful comments.

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Authors and Affiliations

  1. Institut für Experimentelle Mathematik, Universität Duisburg-Essen, Thea-Leymann-Straße 9, 45127, Essen, Germany

    Tran van Trung

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  1. Tran van Trung
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Correspondence to Tran van Trung.

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Communicated by L. Teirlinck.

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van Trung, T. A recursive construction for simple t-designs using resolutions. Des. Codes Cryptogr. 86, 1185–1200 (2018). https://doi.org/10.1007/s10623-017-0389-6

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