Constacyclic Codes and Some New Quantum MDS Codes

One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. Quantum maximal distance separable (MDS) codes are optimal in the sense they attain maximal minimum distance. Recently, constructing quantum MDS codes has received much attention and seems...

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Veröffentlicht in:	IEEE transactions on information theory 2014-04, Vol.60 (4), p.2080-2086
Hauptverfasser:	Kai, Xiaoshan, Zhu, Shixin, Li, Ping
Format:	Artikel
Sprache:	eng
Schlagworte:	Applied sciences Constacyclic codes cyclotomic cosets Educational institutions Error correction codes Exact sciences and technology Generators Information theory Information, signal and communications theory Linear codes Polynomials quantum MDS codes Quantum mechanics Quantum theory Telecommunications and information theory Vectors
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Zusammenfassung:	One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. Quantum maximal distance separable (MDS) codes are optimal in the sense they attain maximal minimum distance. Recently, constructing quantum MDS codes has received much attention and seems to become more and more difficult. In this paper, based on classical constacyclic codes, we construct some new quantum MDS codes by employing the Hermitian construction. Compared with the known quantum MDS codes, these quantum MDS codes have much larger minimum distance.
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2014.2308180