On the symmetry group of the Mollard code

Abstract

For a pair of given binary perfect codes C and D of lengths t and m respectively, the Mollard construction outputs a perfect code M (C, D) of length tm + t + m, having subcodes C 1 and D 2 , that are obtained from codewords of C and D respectively by adding appropriate number of zeros. In this work we generalize of a result for symmetry groups of Vasil'ev codes [2] and find the group Stab D 2 Sym(M (C, D)). The result is preceded by and partially based on a discussion of "linearity" of coordinate positions (points) in a nonlinear perfect code (non-projective Steiner triple system respectively).

On separability of the classes of homogeneous and transitive perfect binary codes

“…The Mollard codes are a generalization of Vasil'ev codes, and the theorem is easily proved taking into account the structure of the Steiner triple system of a Mollard code, which is described in detail, e.g., in [13]. Thus, homogeneous nontransitive perfect codes can be produced by using the Mollard construction, though it should be noted that this is technically much more difficult than what was done above.…”