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New Optimal Asymmetric Quantum Codes Derived from Negacyclic Codes

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Abstract

The construction of quantum maximum-distance-separable (MDS) codes have been studied by many researchers for many years. Here, by using negacyclic codes, we construct two families of asymmetric quantum codes. The first family is the asymmetric quantum codes with parameters \([[q^{2}+1,q^{2}+1-2(t+k+1),(2k+2)/(2t+2)]]_{q^{2}}\), where 0≤t≤k≤(q−1)/2, \(q \equiv1(\operatorname{mod} 4)\), and k, t are positive integers. The second one is the asymmetric quantum codes with parameters \([[(q^{2}+1)/2,(q^{2}+1)/2-2(t+k),(2k+1)/(2t+1)]]_{q^{2}}\), where 1≤t≤k≤(q−1)/2, and k, t are positive integers. Moreover, the constructed asymmetric quantum codes are optimal and different from the codes available in the literature.

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Acknowledgements

The research was supported by the National Science Foundation of China (Grant No. 61003121) and National High Technology Research and Development Program of China (No. 61202084).

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  1. School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Jian-Zhang Chen, Jian-Ping Li & Jie Lin

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  1. Jian-Zhang Chen
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  2. Jian-Ping Li
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  3. Jie Lin
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Correspondence to Jian-Zhang Chen.

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Chen, JZ., Li, JP. & Lin, J. New Optimal Asymmetric Quantum Codes Derived from Negacyclic Codes. Int J Theor Phys 53, 72–79 (2014). https://doi.org/10.1007/s10773-013-1784-z

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