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

2017/01/21 by Cunsheng Ding, Ding, Cunsheng
Engineering · Computer Science · Mathematics · #graph theory and CDMA systems #Coding theory and cryptography #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1701.05965

Abstract

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 ≡ 2 \pmod4 ≥ 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.

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