布西系统和斯坦纳战术问题

Pub Date : 2023-12-27 DOI:10.3336/gm.58.2.04

C. Colbourn, Donald L. Kreher, P. R. Ostergard

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引用次数: 0

摘要

1853 年，斯坦纳提出了一系列组合（战术）问题，最终引发了大量关于斯坦纳系统的研究。然而，斯坦纳问题的解只有在强度为 2 和 3 时才与斯坦纳系统相吻合。对于更大的强度，基本上只有一类斯坦纳战术问题的解是已知的，即布西在一个多世纪前发现的。本文讨论了斯坦纳系统、完美二进制一误校正码和斯坦纳战术问题解（布西系统）之间的关系。对于后者，本文提供了最多 15 个点的计算结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Bussey systems and Steiner's tactical problem

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.

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