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New quantum codes from two linear codes

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Abstract

A CSS quantum code is succinctly represented as a pair of linear codes \((C_1 ,C_2^{\perp })\) over finite fields \({\mathbb {F}}_{p^e}\) with \(C_2^{\perp }\subset C_1\), where p is a prime and e is a positive integer. In this paper, we present two criteria of the \(C_2^{\perp _s}\subset C_1\) , where \(C_2^{\perp _s}\) denotes the s-Galois dual of \(C_2\) and \(0\le s <e\). Then, using the two criteria, we construct some new quantum codes and a class of new quantum maximum-distance-separable (quantum MDS) codes. In addition, our obtained quantum MDS codes have parameters better than the ones available in the literature.

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Acknowledgements

This work was supported by Scientific Research Foundation of Hubei Provincial Education Department of China (Grant No. Q20174503) and the National Science Foundation of Hubei Polytechnic University of China (Grant Nos. 12xjz14A and 17xjz03A).

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Correspondence to Peng Hu.

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Liu, X., Hu, P. New quantum codes from two linear codes. Quantum Inf Process 19, 78 (2020) doi:10.1007/s11128-020-2575-0

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Keywords

  • s-Galois dual code
  • Quantum MDS code
  • Rank of matrix