Propelinear codes related to some classes of optimal codes

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 $\mathbb Z_4$-linear Preparata code to the $\mathbb Z_4$-linear perfect code.