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

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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.

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  1. Institute for Information Transmission Problems, RAS, Moscow

    V. A. Zinoviev & D. V. Zinoviev

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  1. V. A. Zinoviev
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  2. D. V. Zinoviev
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Translated from Problemy Peredachi Informatsii, No. 4, 2004, pp. 48–67.

Original Russian Text Copyright © 2004 by V. Zinoviev, D. Zinoviev.

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Zinoviev, V.A., Zinoviev, D.V. Classification of Steiner quadruple systems of order 16 and rank at most 131. Probl Inf Transm 40, 337–355 (2004). https://doi.org/10.1007/s11122-005-0003-9

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  • DOI: https://doi.org/10.1007/s11122-005-0003-9

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