On binary 1-perfect additive codes: some structural properties

The rank and kernel of 1-perfect additive codes is determined. Additive codes could be seen as translation-invariant propelinear codes and, in this correspondence, a characterization of propelinear codes as codes having a regular subgroup of the full group of isometries of the code is established. A characterization of the automorphism group of a 1-perfect additive code is given and also the cardinality of this group is computed. Finally, an efficiently computable characterization of the Steiner triple systems associated with a 1-perfect binary additive code is also established. Index Terms--Additive codes, automorphism group, kernel, 1-perfect codes, rank.