## Abstract

Some infinite families of systems of linked symmetric designs (or SLSDs, for short) were constructed by Cameron and Seidel (Proc. Kon. Nederl. Akad. Wetensch. (A) 76 (1973) 1-8) using quadratic and bilinear forms over GF(2). The smallest of these systems was used by Preece and Cameron (Utilitas Math. 8 (1975) 193-204) to construct certain designs (which they called fully balanced hyper-graeco-latin Youden 'squares'). The purpose of this paper is to construct an infinite sequence of closely related designs (here called multi-letter Youden rectangles) from the SLSDs of Cameron and Seidel. These rectangles are k×v, with v=2
^{2n} and k=2
^{2n-1}±2
^{n-1}. The paper also provides a non-trivial example of how to translate from the combinatorial view of designs (sets with incidence relations) to the statistical (sets with partitions).

Original language | English |
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Pages (from-to) | 143-151 |

Number of pages | 9 |

Journal | Discrete Mathematics |

Volume | 266 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 6 May 2003 |

## Keywords

- 1-factorisation
- Quadratic form
- Symmetric design
- Youden square