Construction of Minimal Tail-Biting Trellises for Codes over Finite Abelian Groups
<|reference_start|>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.<|reference_end|>
@article{yang2007construction,
    title={Construction of Minimal Tail-Biting Trellises for Codes over Finite
  Abelian Groups},
    author={Qinqin Yang and Zhongping Qin},
    journal={arXiv preprint arXiv:cs/0702020},
    year={2007},
    archivePrefix={arXiv},
    eprint={cs/0702020},
    primaryClass={cs.IT math.IT}
}