  A definition of atomic codeword for a group code is presented. Some
properties of atomic codewords of group codes are investigated. Using these
properties, it is shown that every minimal tail-biting trellis for a group code
over a finite abelian group can be constructed from its characteristic
generators, which extends the work of Koetter and Vardy who treated the case of
a linear code over a field. We also present an efficient algorithm for
constructing the minimal tail-biting trellis of a group code over a finite
abelian group, given a generator matrix.
