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arXiv 1701.05965cs.ITmath.COmath.IT
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循环码的Steiner系统$S(2, 4, 2^m)$的无限族

An infinite family of Steiner systems $S(2, 4, 2^m)$ from cyclic codes

Cunsheng Ding

备注：
arXiv admin note: text overlap with arXiv:1605.03796
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摘要：

斯坦纳系统是组合数学中一个很吸引人的话题。研究最多的Steiner系统是$S(2, 3, v)$（Steiner三元系统）、$S(3, 4, v)$（Steiner四元系统）和$S(2, 4, v)$。在文献中有几个无限族的Steiner系统$S(2, 4, v)$。本文的目的是对循环码中的所有$m \equiv 2 \pmod{4} \geq 6$给出一个无限族的Steiner系统$S(2, 4, 2^m)$.这可能是第一个编码理论的建设一个无限家庭的施泰纳系统$S(2, 4, v)$。作为一个副产品，许多无限族的$2$ -设计，本文也报道。

英文摘要：

Steiner systems are a fascinating topic of combinatorics. The most studied Steiner systems are $S(2, 3, v)$ (Steiner triple systems), $S(3, 4, v)$ (Steiner quadruple systems), and $S(2, 4, v)$. There are a few infinite families of Steiner systems $S(2, 4, v)$ in the literature. The objective of this paper is to present an infinite family of Steiner systems $S(2, 4, 2^m)$ for all $m \equiv 2 \pmod{4} \geq 6$ from cyclic codes. This may be the first coding-theoretic construction of an infinite family of Steiner systems $S(2, 4, v)$. As a by-product, many infinite families of $2$-designs are also reported in this paper.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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