We obtain a necessary and sufficient condition for that there exists a nontrivial self-orthogonal or self-dual cyclic codes over finite fields and the explicit enumerating formula. As a corollary, a simple and easy criterion for several classes of non-trivial self-orthogonal cyclic codes is given.
Qun Ying LIAO, Yan Bin LI, Huan LIAO.
The Existence for Self-Orthogonal Cyclic Codes over Finite Fields. Acta Mathematica Sinica, Chinese Series, 2014, 57(1): 117-124 https://doi.org/10.12386/A2014sxxb0011
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