Multi-letter Youden rectangles from quadratic forms

Peter J. Cameron*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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 languageEnglish
Pages (from-to)143-151
Number of pages9
JournalDiscrete Mathematics
Issue number1-3
Publication statusPublished - 6 May 2003


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


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