Classification of Cyclic Steiner Quadruple Systems

Yanxun Chang; Bingli Fan; Tao Feng; Derek F. Holt; Patric R J Östergård

doi:10.1002/jcd.21530

Classification of Cyclic Steiner Quadruple Systems

Yanxun Chang, Bingli Fan, Tao Feng, Derek F. Holt, Patric R J Östergård

Information Theory

Research output: Contribution to journal › Article › Scientific › peer-review

4 Citations (Scopus)

Abstract

The problem of classifying cyclic Steiner quadruple systems (CSQSs) is considered. A computational approach shows that the number of isomorphism classes of such designs with orders 26 and 28 is 52,170 and 1,028,387, respectively. It is further shown that CSQSs of order 2p, where p is a prime, are isomorphic iff they are multiplier equivalent. Moreover, no CSQSs of order less than or equal to 38 are isomorphic but not multiplier equivalent.

Original language	English
Number of pages	19
Journal	Journal of Combinatorial Designs
Volume	25
Issue number	3
Early online date	5 Aug 2016
DOIs	https://doi.org/10.1002/jcd.21530
Publication status	Published - Mar 2017
MoE publication type	A1 Journal article-refereed

Keywords

Cyclic design
Steiner quadruple system
Transitive permutation group

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10.1002/jcd.21530

http://wrap.warwick.ac.uk/80062/

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AB - The problem of classifying cyclic Steiner quadruple systems (CSQSs) is considered. A computational approach shows that the number of isomorphism classes of such designs with orders 26 and 28 is 52,170 and 1,028,387, respectively. It is further shown that CSQSs of order 2p, where p is a prime, are isomorphic iff they are multiplier equivalent. Moreover, no CSQSs of order less than or equal to 38 are isomorphic but not multiplier equivalent.

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KW - Transitive permutation group

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Classification of Cyclic Steiner Quadruple Systems

Abstract

Keywords

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