Quantum codes from cyclic codes over the ring Fp[u]/〈u3 − u〉

Tushar Bag; Ashish K. Upadhyay; Mohammad Ashraf; Ghulam Mohammad

doi:10.1142/s1793557120500084

Quantum codes from cyclic codes over the ring Fp[u]/〈u3 − u〉

Asian-European Journal of Mathematics ◽

10.1142/s1793557120500084 ◽

2019 ◽

Vol 12 (07) ◽

pp. 2050008

Author(s):

Tushar Bag ◽

Ashish K. Upadhyay ◽

Mohammad Ashraf ◽

Ghulam Mohammad

Keyword(s):

Cyclic Codes ◽

Quantum Codes ◽

Orthogonal Property

In this paper, we study nonbinary quantum codes from cyclic codes over the ring [Formula: see text] for odd prime [Formula: see text]. We give the constructional properties of linear and cyclic codes over the ring [Formula: see text]. As an applications of these classes of codes, we obtain quantum codes over [Formula: see text] using self-orthogonal property. Moreover, we find some new nonbinary quantum codes with better parameters than the known quantum codes over [Formula: see text].

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Quantum Codes Derived from One-Generator Quasi-Cyclic Codes with Hermitian Inner Product

International Journal of Theoretical Physics ◽

10.1007/s10773-019-04324-z ◽

2019 ◽

Vol 59 (1) ◽

pp. 300-312 ◽

Cited By ~ 1

Author(s):

Jingjie Lv ◽

Ruihu Li ◽

Junli Wang

Keyword(s):

Cyclic Codes ◽

Inner Product ◽

Quantum Codes ◽

Hermitian Inner Product ◽

Quasi Cyclic Codes

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ON TWO PROBLEMS OF ASYMMETRIC QUANTUM CODES

International Journal of Modern Physics B ◽

10.1142/s0217979214500179 ◽

2014 ◽

Vol 28 (06) ◽

pp. 1450017 ◽

Cited By ~ 6

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.

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