Publication date: 27 December 2023
Volume: Vol 58
Issue: Svezak 2
Pages: 201-224
DOI: 10.3336/gm.58.2.04
Original scientific paper
https://doi.org/10.3336/gm.58.2.04
Bussey systems and Steiner's tactical problem
Charles J Colbourn
orcid.org/0000-0002-3104-9515
; Arizona State University, Tempe, Arizona, USA
Donald L Kreher
orcid.org/0000-0002-5031-9410
; Michigan Technological University, Houghton, Michigan, USA
Patric R. J Ostergård
orcid.org/0000-0003-0426-9771
; Department of Information and Communications Engineering, Aalto University School of Electrical Engineering, 00076 Aalto, Finland
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.
Steiner system, original Steiner system, Bussey system, perfect code
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23.12.2024.
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