A Note on Characteristic Generators of a Free Cyclic Code and Its Dual

摘要

Let C be a free cyclic code over Zpα and dimp C = k. In the paper, we prove that if the k characteristic generators of C are p-linearly independent then the corresponding nα-k char-acteristic 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 Zpα .