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On extending propelinear structures of the Nordstrom–Robinson code to the Hamming code

  • Coding Theory
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Abstract

A code is said to be propelinear if its automorphism group contains a subgroup which acts on the codewords regularly. Such a subgroup is called a propelinear structure on the code. With the aid of computer, we enumerate all propelinear structures on the Nordstrom–Robinson code and analyze the problem of extending them to propelinear structures on the extended Hamming code of length 16. The latter result is based on the description of partitions of the Hamming code of length 16 into Nordstrom–Robinson codes via Fano planes, presented in the paper. As a result, we obtain a record-breaking number of propelinear structures in the class of extended perfect codes of length 16.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

    I. Yu. Mogil’nykh

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Correspondence to I. Yu. Mogil’nykh.

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Original Russian Text © I.Yu. Mogil’nykh, 2016, published in Problemy Peredachi Informatsii, 2016, Vol. 52, No. 3, pp. 97–107.

The results of Section 3 of the paper are obtained under the support of the Russian Foundation for Basic Research, project no. 13-01-00463; results of Section 4 are funded by the Russian Science Foundation, project no. 14-11-00555.

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Mogil’nykh, I.Y. On extending propelinear structures of the Nordstrom–Robinson code to the Hamming code. Probl Inf Transm 52, 289–298 (2016). https://doi.org/10.1134/S0032946016030078

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  • DOI: https://doi.org/10.1134/S0032946016030078

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