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Generalized Preparata codes and 2-resolvable Steiner quadruple systems

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Abstract

We consider generalized Preparata codes with a noncommutative group operation. These codes are shown to induce new partitions of Hamming codes into cosets of these Preparata codes. The constructed partitions induce 2-resolvable Steiner quadruple systems S(n, 4, 3) (i.e., systems S(n, 4, 3) that can be partitioned into disjoint Steiner systems S(n, 4, 2)). The obtained partitions of systems S(n, 4, 3) into systems S(n, 4, 2) are not equivalent to such partitions previously known.

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  1. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    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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Correspondence to V. A. Zinoviev.

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Original Russian Text cV.A. Zinoviev, D.V. Zinoviev, 2016, published in Problemy Peredachi Informatsii, 2016, Vol. 52, No. 2, pp. 15–36.

The research was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Science Foundation, project no. 14-50-00150.

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Zinoviev, V.A., Zinoviev, D.V. Generalized Preparata codes and 2-resolvable Steiner quadruple systems. Probl Inf Transm 52, 114–133 (2016). https://doi.org/10.1134/S0032946016020022

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  • DOI: https://doi.org/10.1134/S0032946016020022

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