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On the Generalized Concatenated Construction for the Nordstrom–Robinson Code and the Binary Golay Code

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Abstract

We show that the Nordstrom–Robinson code and the extended binary Golay code are generalized concatenated codes of order 3.

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Acknowledgment

The authors are grateful Denis Krotov for a stimulating conversation on the representation of the Nordstrom–Robinson code as a GC code of the third order, which resulted in this paper, and also to an anonymous reviewer for many useful remarks, which have been used in the final version of the paper.

Funding

The research was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences; it was supported by the Russian Foundation for Basic Research, project no. 19-01-00364, and the Bulgarian National Science Fund, project no. 20-51-18002.

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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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Translated from Problemy Peredachi Informatsii, 2021, Vol. 57, No. 4, pp. 34–44 https://doi.org/10.31857/S0555292321040033.

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Zinoviev, V., Zinoviev, D. On the Generalized Concatenated Construction for the Nordstrom–Robinson Code and the Binary Golay Code. Probl Inf Transm 57, 331–340 (2021). https://doi.org/10.1134/S0032946021040037

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  • DOI: https://doi.org/10.1134/S0032946021040037

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