A family of highly symmetric codes

We define a class of codes admitting a large automorphism group. This family contains the binary extended Hamming code, the hexacode, the Golay codes, the Pless symmetry codes, as well as the [[16, 4, 12].sub.8]-codes constructed by Marcugini et al. A computer search resulted in the construction of codes with new parameters [[28, 7, 18].sup.8], [[32, 8, 20].sup.8], and [[39, 13, 17].sup.4] belonging to this family. Index Terms--Linear codes, Galois fields, symmetry groups.