Abstract
Let C be a free cyclic code over Z n α and dim p C = k. In the paper, we prove that if the k characteristic generators of C are p-linearly independent then the corresponding nα − k characteristic generators of C ⊥ are p-linearly independent. We then show that to any trellis that can be constructed from k p-linearly independent characteristic generators of C, there exists a trellis for C ⊥ with the same state-complexity profile, which generalizes the conjecture of Koetter and Vardy to a free cyclic code over Z n α.
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Foundation item: Supported by the National Natural Science Foundation of China(60673071)
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Yang, Q., Qin, Z. A note on characteristic generators of a free cyclic code and its dual. Wuhan Univ. J. Nat. Sci. 14, 14–18 (2009). https://doi.org/10.1007/s11859-009-0104-1
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DOI: https://doi.org/10.1007/s11859-009-0104-1