Construction of Minimal Tail-Biting Trellises for Codes over Finite Abelian Groups
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.
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