Abstract
A code is said to be propelinear if its automorphism group contains a subgroup that acts regularly on codewords. We show propelinearity of complements of cyclic codes C 1,i , (i, 2m − 1) = 1, of length n = 2m − 1, including the primitive two-error-correcting BCH code, to the Hamming code; the Preparata code to the Hamming code; the Goethals code to the Preparata code; and the Z4-linear Preparata code to the Z4-linear perfect code.
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The research was carried out at the expense of the Russian Science Foundation, project no. 14-11-00555.
Original Russian Text © I.Yu. Mogilnykh, F.I. Solov’eva, 2017, published in Problemy Peredachi Informatsii, 2017, Vol. 53, No. 3, pp. 54–63.
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Mogilnykh, I.Y., Solov’eva, F.I. Propelinear codes related to some classes of optimal codes. Probl Inf Transm 53, 251–259 (2017). https://doi.org/10.1134/S0032946017030061
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DOI: https://doi.org/10.1134/S0032946017030061