Symplectic self-orthogonal quasi-cyclic codes
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In this paper, we obtain necessary and sufficient conditions for quasi-cyclic codes with index even to be symplectic self-orthogonal. Then, we propose a method for constructing symplectic self-orthogonal quasi-cyclic codes, which allows arbitrary polynomials that divide x^n-1 to construct symplectic self-orthogonal codes. Finally, we construct many binary symplectic self-orthogonal codes with excellent parameters, corresponding to over a hundred record-breaking quantum codes, improving Grassl's table (bounds on the minimum distance of quantum codes. http://www.codetables.de).
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