Concatenated group codes and their exponents

Codes that are concatenations of group codes are considered. It is shown that when
G
and
H
are finite groups and the inner and outer codes are
G-
and
H-
codes, respectively, then under certain conditions the concatenated code is a
G \times H
code. A necessary and sufficient condition is given for a
G \times H
code to have a structure as a concatenated code. Further, under the assumption that all group algebras involved are semisimple, it is shown how the character of a concatenated code can be expressed in terms of the characters of the inner and outer codes. This leads to an application of a result by Ward [5] which enables one to find (or lower bound) the exponent of the concatenated code by a computation on characters of
G
and
H
. In an example this result enables the improvement of the usual minimum distance bound on concatenated codes. A general upper bound on the exponent of concatenated group codes is proved, and it is shown to be tight by an example.