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On Affine-Invariant Two-Fold Quadruple Systems

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Abstract

In this paper, we present a direct construction and a recursive construction of the affine-invariant 2-fold quadruple systems of order q (3-(q, 4, 2) designs), where q is a prime power. The direct construction also gives a criterion for the existence of affine-invariant 2-fold quadruple systems of prime order by using 1-factors of graphs. By our recursive construction, an infinite family of affine-invariant 2-fold quadruple systems is established by using our previous direct construction.

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Acknowledgments

The author would thank the anonymous referees for the valuable comments. The author also would like to express his appreciation to Professor Masakazu Jimbo for his advice and encouragement. This work was supported in part by JSPS under Grant-in-Aid for JSPS Fellows No. 26011700.

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  1. Japan Society for the Promotion of Science, Graduate School of Information Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8601, Japan

    Xiao-Nan Lu

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  1. Xiao-Nan Lu
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Lu, XN. On Affine-Invariant Two-Fold Quadruple Systems. Graphs and Combinatorics 31, 1915–1927 (2015). https://doi.org/10.1007/s00373-015-1595-5

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