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Special overlarge sets of Kirkman triple systems

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Abstract

A Steiner quadruple system of order \(v+1\) with resolvable derived designs (every derived Steiner triple system of order v at a point is resolvable), abbreviated as RDSQS\((v+1)\), has been used to construct a large set of Kirkman triple systems of order 3v. In this paper, an RDSQS\((v+1)\) is reduced to an overlarge set of Kirkman triple systems of order v with an additional property (OLKTS\(^+(v)\)), which plays the same role in constructing an LKTS(3v) as an RDSQS\((v+1)\). Some recursive constructions of OLKTS\(^+\)s are also established. As a result, some infinite classes of OLKTS\(^+\)s and LKTSs are obtained.

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Authors and Affiliations

  1. Department of Mathematics, Soochow University, Suzhou, 215006, China

    Juanjuan Xu & Lijun Ji

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  1. Juanjuan Xu
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  2. Lijun Ji
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Correspondence to Juanjuan Xu.

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Communicated by J. Jedwab.

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Research is supported by NSFC grants 11871363, 12271390 (L. Ji), The Natural Science Foundation of the Jiangsu Higher Education Institutions of China SZ10760423 (J. Xu).

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Xu, J., Ji, L. Special overlarge sets of Kirkman triple systems. Des. Codes Cryptogr. (2024). https://doi.org/10.1007/s10623-024-01386-x

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