Propelinear codes related to some classes of optimal codes

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, 2^m − 1) = 1, of length n = 2^m − 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.