Abstract
In this paper, we consider a family of one-generator quasi-cyclic codes and their applications in quantum codes construction. We give a sufficient condition for self-orthogonality with respect to Hermitian inner product. By virtue of the well-known MacWilliams equations, some binary and ternary stabilizer quantum codes with good parameters are constructed. Furthermore, we present a lower bound on the Hermitian dual distance of these involved codes. As the computational results, some good stabilizer quantum codes over small finite fields are obtained.
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Acknowledgments
This work is supported by National Natural Science Foundation of China (Nos.11471011, 11801564) and Natural Science Foundation of Shaanxi (No.2017JQ1032).
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Lv, J., Li, R. & Wang, J. Quantum Codes Derived from One-Generator Quasi-Cyclic Codes with Hermitian Inner Product. Int J Theor Phys 59, 300–312 (2020). https://doi.org/10.1007/s10773-019-04324-z
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DOI: https://doi.org/10.1007/s10773-019-04324-z