Non-binary quantum codes constructed from classical BCH codes

By studying the properties of [Formula: see text]-cyclotomic cosets, the maximum designed distances of Hermitian dual-containing constacyclic Bose–Chaudhuri–Hocquenghem (BCH) codes with length [Formula: see text] are determined, where [Formula: see text] is an odd prime power and [Formula: see text] is an integer. Further, their dimensions are calculated precisely for the given designed distance. Consequently, via Hermitian Construction, many new quantum codes could be obtained from these codes, which are not covered in the literature.

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New families of asymmetric quantum BCH codes

Quantum Information and Computation ◽

10.26421/qic11.3-4-4 ◽

2011 ◽

Vol 11 (3&4) ◽

pp. 239-252

Author(s):

Giuliano G. La Guardia

Keyword(s):

Phase Shift ◽

Quantum Systems ◽

Bch Codes ◽

Quantum Codes ◽

Asymmetric Quantum ◽

The Asymmetry ◽

Better Than

Several families of nonbinary asymmetric quantum Bose-Chaudhuri-Hocquenghem (BCH) codes are presented in this paper. These quantum codes have parameters better than the ones available in the literature. Additionally, such codes can be applied in quantum systems where the asymmetry between qudit-flip and phase-shift errors is large.

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Hermitian dual-containing narrow-sense constacyclic BCH codes and quantum codes

Quantum Information Processing ◽

10.1007/s11128-019-2440-1 ◽

2019 ◽

Vol 18 (10) ◽

Author(s):

Liqi Wang ◽

Zhonghua Sun ◽

Shixin Zhu

Keyword(s):

Bch Codes ◽

Quantum Codes ◽

Narrow Sense

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Asymmetric Quantum Codes of Large Z - Distance Constructed from a Class of Quaternary Imprimitive BCH Codes

2015 Fifth International Conference on Instrumentation and Measurement, Computer, Communication and Control (IMCCC) ◽

10.1109/imccc.2015.121 ◽

2015 ◽

Author(s):

Ruihu Li ◽

Gen Xu ◽

Qiang Fu ◽

Fei Zuo

Keyword(s):

Bch Codes ◽

Quantum Codes ◽

Asymmetric Quantum ◽

Asymmetric Quantum Codes

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New quantum codes derived from a family of antiprimitive BCH codes

International Journal of Quantum Information ◽

10.1142/s0219749917500526 ◽

2017 ◽

Vol 15 (07) ◽

pp. 1750052 ◽

Cited By ~ 2

Author(s):

Yang Liu ◽

Ruihu Li ◽

Liangdong Lü ◽

Luobin Guo

Keyword(s):

Information Theory ◽

Quantum Information ◽

Detailed Analysis ◽

Communication System ◽

Quantum Information Theory ◽

Bch Codes ◽

Quantum Codes ◽

Narrow Sense ◽

Classical Communication ◽

Cyclotomic Cosets

The Bose–Chaudhuri–Hocquenghem (BCH) codes have been studied for more than 57 years and have found wide application in classical communication system and quantum information theory. In this paper, we study the construction of quantum codes from a family of [Formula: see text]-ary BCH codes with length [Formula: see text] (also called antiprimitive BCH codes in the literature), where [Formula: see text] is a power of 2 and [Formula: see text]. By a detailed analysis of some useful properties about [Formula: see text]-ary cyclotomic cosets modulo [Formula: see text], Hermitian dual-containing conditions for a family of non-narrow-sense antiprimitive BCH codes are presented, which are similar to those of [Formula: see text]-ary primitive BCH codes. Consequently, via Hermitian Construction, a family of new quantum codes can be derived from these dual-containing BCH codes. Some of these new antiprimitive quantum BCH codes are comparable with those derived from primitive BCH codes.

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New quantum codes constructed from quaternary BCH codes

Quantum Information Processing ◽

10.1007/s11128-016-1397-6 ◽

2016 ◽

Vol 15 (10) ◽

pp. 4099-4116 ◽

Cited By ~ 3

Author(s):

Gen Xu ◽

Ruihu Li ◽

Luobin Guo ◽

Yuena Ma

Keyword(s):

Bch Codes ◽

Quantum Codes

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A class of negacyclic BCH codes and its application to quantum codes

Designs Codes and Cryptography ◽

10.1007/s10623-017-0441-6 ◽

2017 ◽

Vol 86 (10) ◽

pp. 2139-2165 ◽

Cited By ~ 8

Author(s):

Shixin Zhu ◽

Zhonghua Sun ◽

Ping Li

Keyword(s):

Bch Codes ◽

Quantum Codes

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NEW QUANTUM CODES CONSTRUCTED FROM A CLASS OF IMPRIMITIVE BCH CODES

International Journal of Quantum Information ◽

10.1142/s0219749913500068 ◽

2013 ◽

Vol 11 (01) ◽

pp. 1350006 ◽

Cited By ~ 5

Author(s):

YANG LIU ◽

YUENA MA ◽

YOUQIAN FENG ◽

RUIHU LI

Keyword(s):

Lower Bound ◽

Prime Power ◽

Careful Analysis ◽

Bch Codes ◽

Bch Code ◽

Quantum Codes ◽

Narrow Sense ◽

Cyclotomic Cosets ◽

Steane Construction ◽

Better Than

By a careful analysis on cyclotomic cosets, the maximal designed distance δnew of narrow-sense imprimitive Euclidean dual containing q-ary BCH code of length [Formula: see text] is determined, where q is a prime power and l is odd. Our maximal designed distance δnew of dual containing narrow-sense BCH codes of length n improves upon the lower bound δmax for maximal designed distances of dual containing narrow-sense BCH codes given by Aly et al. [IEEE Trans. Inf. Theory53 (2007) 1183]. A series of non-narrow-sense dual containing BCH codes of length n, including the ones whose designed distances can achieve or exceed δnew, are given, and their dimensions are computed. Then new quantum BCH codes are constructed from these non-narrow-sense imprimitive BCH codes via Steane construction, and these new quantum codes are better than previous results in the literature.

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