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The methods for constructing quantum codes is not always sufficient by itself. Also, the constructed quantum codes as in the classical coding theory have to enjoy a quality of its parameters that play a very important role in recovering data efficiently. In a very recent study quantum construction and examples of quantum codes over a finite field of order $q$ are presented by La Garcia in \cite{Guardia}. Being inspired by La Garcia's the paper, here we extend the results over a finite field with $q^2$ elements by studying necessary and sufficient conditions for constructions quantum codes over this field. We determine a criteria for the existence of $q^2$-cyclotomic cosets containing at least three elements and present a construction method for quantum maximum-distance separable (MDS) codes. Moreover, we derive a way to construct quantum codes and show that this construction method leads to quantum codes with better parameters than the ones in \cite{Guardia}.
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참고문헌 (22)
참고문헌 신청
S. A. Aly / 2007 / On quantum and classical BCH codes / IEEE Trans. Inform. Theory 53(3):1183~1188
A. Ashikhmin / 2001 / Nonbinary quantum stabilizer codes / IEEE Trans. Inform. Theory 47(7):3065~3072
N. Aydin / 2001 / The structure of 1-generator quasi-twisted codes and new linear codes / Des. Codes Cryptogr 24(3):313~326
J.-Z. Chen / 2014 / New optimal asymmetric quantum codes derived from negacyclic codes / Internat. J. Theoret. Phys 53(1):72~79
J. Gao / 2018 / Quantum codes derived from negacyclic codes / Internat. J. Theoret. Phys 57(3):682~686
A. Ashikhmin / 2001 / Nonbinary quantum stabilizer codes / IEEE Trans. Inform. Theory 47(7):3065~3072
N. Aydin / 2001 / The structure of 1-generator quasi-twisted codes and new linear codes / Des. Codes Cryptogr 24(3):313~326
J.-Z. Chen / 2014 / New optimal asymmetric quantum codes derived from negacyclic codes / Internat. J. Theoret. Phys 53(1):72~79
J. Gao / 2018 / Quantum codes derived from negacyclic codes / Internat. J. Theoret. Phys 57(3):682~686
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