Bussey systems and Steiner's tactical problem

Charles J. Colbourn, Donald L. Kreher, Patric R.J. Östergård

Research output: Contribution to journalArticleScientificpeer-review


In 1853, Steiner posed a number of combinatorial (tactical) problems, which eventually led to a large body of research on Steiner systems. However, solutions to Steiner’s questions coincide with Steiner systems only for strengths two and three. For larger strengths, essentially only one class of solutions to Steiner’s tactical problems is known, found by Bussey more than a century ago. In this paper, the relationships among Steiner systems, perfect binary one-error-correcting codes, and solutions to Steiner’s tactical problem (Bussey systems) are discussed. For the latter, computational results are provided for at most 15 points.

Original languageEnglish
Pages (from-to)201-224
Number of pages24
JournalGlasnik Matematicki
Issue number2
Publication statusPublished - 2023
MoE publication typeA1 Journal article-refereed


  • Bussey system
  • original Steiner system
  • perfect code
  • Steiner system


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