Classification of Steiner quadruple systems of order 16 and rank at most 131

Classification of Steiner quadruple systems of order 16 and rank at most 131 A Steiner quadruple system SQS(v) of order v is a 3-design T (v, 4, 3, λ) with λ = 1. In this paper we describe all nonisomorphic systems SQS(16) that can be obtained by the generalized concatenated construction (GC-construction). These Steiner systems have rank at most 13 over $$ \mathbb{F} $$ 2. In particular, there is one system SQS(16) of rank 11 (points and planes of the a fine geometry AG(4, 2)), fifteen systems of rank 12, and 4131 systems of rank 13. All these Steiner systems are resolvable. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Classification of Steiner quadruple systems of order 16 and rank at most 131

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Publisher
Springer Journals
Copyright
Copyright © 2004 by MAIK “Nauka/Interperiodica”
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1007/s11122-005-0003-9
Publisher site
See Article on Publisher Site

Abstract

A Steiner quadruple system SQS(v) of order v is a 3-design T (v, 4, 3, λ) with λ = 1. In this paper we describe all nonisomorphic systems SQS(16) that can be obtained by the generalized concatenated construction (GC-construction). These Steiner systems have rank at most 13 over $$ \mathbb{F} $$ 2. In particular, there is one system SQS(16) of rank 11 (points and planes of the a fine geometry AG(4, 2)), fifteen systems of rank 12, and 4131 systems of rank 13. All these Steiner systems are resolvable.

Journal

Problems of Information TransmissionSpringer Journals

Published: Feb 26, 2005

References

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