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An Infinite Family of Steiner Systems S ( 2 , 4 , 2 m ) from Cyclic Codes
Author(s) -
Ding Cunsheng
Publication year - 2018
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21565
Subject(s) - steiner system , mathematics , steiner tree problem , combinatorics , discrete mathematics
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 ( mod 4 ) ≥ 6 from cyclic codes. As a by‐product, many infinite families of 2‐designs are also reported in this paper.