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On the symmetry group of the Mollard code

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Abstract

We study the symmetry group of a binary perfect Mollard code M(C,D) of length tm + t + m containing as its subcodes the codes C 1 and D 2 formed from perfect codes C and D of lengths t and m, respectively, by adding an appropriate number of zeros. For the Mollard codes, we generalize the result obtained in [1] for the symmetry group of Vasil’ev codes; namely, we describe the stabilizer

$$Sta{b_{{D^2}}}$$

Sym(M(C,D)) of the subcode D 2 in the symmetry group of the code M(C,D) (with the trivial function). Thus we obtain a new lower bound on the order of the symmetry group of the Mollard code. A similar result is established for the automorphism group of Steiner triple systems obtained by the Mollard construction but not necessarily associated with perfect codes. To obtain this result, we essentially use the notions of “linearity” of coordinate positions (points) of a nonlinear perfect code and a nonprojective Steiner triple system.

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Authors and Affiliations

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

    I. Yu. Mogilnykh & F. I. Solov’eva

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  1. I. Yu. Mogilnykh
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  2. F. I. Solov’eva
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Correspondence to I. Yu. Mogilnykh.

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Original Russian Text © I.Yu. Mogilnykh, F.I. Solov’eva, 2016, published in Problemy Peredachi Informatsii, 2016, Vol. 52, No. 3, pp. 73–83.

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Mogilnykh, I.Y., Solov’eva, F.I. On the symmetry group of the Mollard code. Probl Inf Transm 52, 265–275 (2016). https://doi.org/10.1134/S0032946016030042

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  • DOI: https://doi.org/10.1134/S0032946016030042

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