scholarly journals Some families of asymmetric quantum codes and quantum convolutional codes from constacyclic codes

2015 ◽  
Vol 475 ◽  
pp. 186-199 ◽  
Author(s):  
Jianzhang Chen ◽  
Jianping Li ◽  
Yuanyuan Huang ◽  
Jie Lin
Keyword(s):  
Convolutional Codes ◽  
Quantum Codes ◽  
Constacyclic Codes ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes

scholarly journals New optimal asymmetric quantum codes from constacyclic codes

2014 ◽  
Vol 28 (15) ◽  
pp. 1450126 ◽  
Author(s):  
Guanghui Zhang ◽  
Bocong Chen ◽  
Liangchen Li
Keyword(s):  
Prime Power ◽  
Quantum Codes ◽  
Constacyclic Codes ◽  
Theor Phys ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes

In this paper, we construct two classes of asymmetric quantum codes by using constacyclic codes. The first class is the asymmetric quantum codes with parameters [[q2 + 1, q2 + 1 - 2(t + k + 1), (2k + 2)/(2t + 2)]]q2 where q is an odd prime power, t, k are integers with [Formula: see text], which is a generalization of [J. Chen, J. Li and J. Lin, Int. J. Theor. Phys. 53 (2014) 72, Theorem 2] in the sense that we do not assume that q ≡1 ( mod 4). The second one is the asymmetric quantum codes with parameters [Formula: see text], where q ≥ 5 is an odd prime power, t, k are integers with 0 ≤ t ≤ k ≤ q - 1. The constructed asymmetric quantum codes are optimal and their parameters are not covered by the codes available in the literature.

scholarly journals On the construction of optimal asymmetric quantum codes

2014 ◽  
Vol 12 (03) ◽  
pp. 1450017 ◽  
Author(s):  
Liqi Wang ◽  
Shixin Zhu
Keyword(s):  
Linear Codes ◽  
Quantum Codes ◽  
Constacyclic Codes ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes

Constacyclic codes are important classes of linear codes that have been applied to the construction of quantum codes. Six new families of asymmetric quantum codes derived from constacyclic codes are constructed in this paper. Moreover, the constructed asymmetric quantum codes are optimal and different from the codes available in the literature.

New optimal asymmetric quantum codes constructed from constacyclic codes

2017 ◽  
Vol 31 (05) ◽  
pp. 1750030 ◽  
Author(s):  
Gen Xu ◽  
Ruihu Li ◽  
Luobin Guo ◽  
Liangdong Lü
Keyword(s):  
Prime Power ◽  
Error Correcting Codes ◽  
Quantum Codes ◽  
Constacyclic Codes ◽  
Code Length ◽  
Theor Phys ◽  
Singleton Bound ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes ◽  
Quantum Error

In this paper, we propose the construction of asymmetric quantum codes from two families of constacyclic codes over finite field [Formula: see text] of code length [Formula: see text], where for the first family, [Formula: see text] is an odd prime power with the form [Formula: see text] ([Formula: see text] is integer) or [Formula: see text] ([Formula: see text] is integer) and [Formula: see text]; for the second family, [Formula: see text] is an odd prime power with the form [Formula: see text] or [Formula: see text] ([Formula: see text] is integer) and [Formula: see text]. As a result, families of new asymmetric quantum codes [Formula: see text] with [Formula: see text] distance larger than [Formula: see text] are obtained, which are not covered by the asymmetric quantum error-correcting codes (AQECCs) in Refs. 32 and 33 [J.-Z. Chen, J.-P. Li and J. Lin, Int. J. Theor. Phys. 53, 72 (2014); L. Wang and S. Zhu, Int. J. Quantum Inf. 12, 1450017 (2014)] that [Formula: see text]. Also, all the newly obtained asymmetric quantum codes are optimal according to the singleton bound for asymmetric quantum codes.

ON TWO PROBLEMS OF ASYMMETRIC QUANTUM CODES

2014 ◽  
Vol 28 (06) ◽  
pp. 1450017 ◽  
Author(s):  
RUIHU LI ◽  
GEN XU ◽  
LUOBIN GUO
Keyword(s):  
Cyclic Codes ◽  
Error Correcting Codes ◽  
Bch Code ◽  
Quantum Codes ◽  
Quantum Code ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes ◽  
Special Cases ◽  
Quantum Error ◽  
Better Than

In this paper, we discuss two problems on asymmetric quantum error-correcting codes (AQECCs). The first one is on the construction of a [[12, 1, 5/3]]2 asymmetric quantum code, we show an impure [[12, 1, 5/3 ]]2 exists. The second one is on the construction of AQECCs from binary cyclic codes, we construct many families of new asymmetric quantum codes with dz> δ max +1 from binary primitive cyclic codes of length n = 2m-1, where δ max = 2⌈m/2⌉-1 is the maximal designed distance of dual containing narrow sense BCH code of length n = 2m-1. A number of known codes are special cases of the codes given here. Some of these AQECCs have parameters better than the ones available in the literature.

New asymmetric quantum codes over $$F_{q}$$ F q

2016 ◽  
Vol 15 (7) ◽  
pp. 2759-2769 ◽  
Author(s):  
Yuena Ma ◽  
Xiaoyi Feng ◽  
Gen Xu
Keyword(s):  
Quantum Codes ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes

scholarly journals Additive Asymmetric Quantum Codes

2011 ◽  
Vol 57 (8) ◽  
pp. 5536-5550 ◽  
Author(s):  
Martianus Frederic Ezerman ◽  
San Ling ◽  
Patrick Sole
Keyword(s):  
Quantum Codes ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes

scholarly journals Xing–Ling codes, duals of their subcodes, and good asymmetric quantum codes

2013 ◽  
Vol 75 (1) ◽  
pp. 21-42 ◽  
Author(s):  
Martianus Frederic Ezerman ◽  
Somphong Jitman ◽  
Patrick Solé
Keyword(s):  
Quantum Codes ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes
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