Construction of new quantum codes via Hermitian dual-containing matrix-product codes
QUANTUM INFORMATION PROCESSING(2020)
摘要
In 2001, Blackmore and Norton introduced an important tool called matrix-product codes, which turn out to be very useful to construct new quantum codes of large lengths. To obtain new and good quantum codes, we first give a general approach to construct matrix-product codes being Hermitian dual-containing and then provide the constructions of such codes in the case s|(q^2-1) , where s is the number of the constituent codes in a matrix-product code. For s| (q+1) , we construct such codes with lengths more flexible than the known ones in the literature. For s| (q^2-1) and s|̸ (q+1) , such codes are constructed in an unusual manner; some of the constituent codes therein are not required to be Hermitian dual-containing. Accordingly, by Hermitian construction, we present two procedures for acquiring quantum codes. Finally, we list some good quantum codes, many of which improve those available in the literature or add new parameters.
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关键词
Hermitian dual-containing codes,Matrix-product codes,Generalized Reed–Solomon codes,Extended generalized Reed–Solomon codes,Quantum codes
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