Constructions of maximum distance separable symbol-pair codes using cyclic and constacyclic codes

Negacyclic codes of length [Formula: see text] over the Galois ring [Formula: see text] are linearly ordered under set-theoretic inclusion, i.e., they are the ideals [Formula: see text], [Formula: see text], of the chain ring [Formula: see text]. This structure is used to obtain the symbol-pair distances of all such negacyclic codes. Among others, for the special case when the alphabet is the finite field [Formula: see text] (i.e., [Formula: see text]), the symbol-pair distance distribution of constacyclic codes over [Formula: see text] verifies the Singleton bound for such symbol-pair codes, and provides all maximum distance separable symbol-pair constacyclic codes of length [Formula: see text] over [Formula: see text].

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Application of constacyclic codes to entanglement-assisted quantum maximum distance separable codes

Quantum Information Processing ◽

10.1007/s11128-018-1978-7 ◽

2018 ◽

Vol 17 (8) ◽

Cited By ~ 11

Author(s):

Yang Liu ◽

Ruihu Li ◽

Liangdong Lv ◽

Yuena Ma

Keyword(s):

Maximum Distance ◽

Constacyclic Codes ◽

Maximum Distance Separable ◽

Maximum Distance Separable Codes

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Symbol-triple distance of repeated-root constacyclic codes of prime power lengths

Journal of Algebra and Its Applications ◽

10.1142/s0219498820502096 ◽

2019 ◽

Vol 19 (11) ◽

pp. 2050209 ◽

Cited By ~ 2

Author(s):

Hai Q Dinh ◽

Sampurna Satpati ◽

Abhay Kumar Singh ◽

Woraphon Yamaka

Keyword(s):

Prime Power ◽

Nonzero Element ◽

Maximum Distance ◽

Constacyclic Codes ◽

Chain Ring ◽

Maximum Distance Separable ◽

Positive Integers

Let [Formula: see text] be an odd prime, [Formula: see text] and [Formula: see text] be positive integers and [Formula: see text] be a nonzero element of [Formula: see text]. The [Formula: see text]-constacyclic codes of length [Formula: see text] over [Formula: see text] are linearly ordered under set theoretic inclusion as ideals of the chain ring [Formula: see text]. Using this structure, the symbol-triple distances of all such [Formula: see text]-constacyclic codes are established in this paper. All maximum distance separable symbol-triple constacyclic codes of length [Formula: see text] are also determined as an application.

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Optimal b-symbol constacyclic codes with respect to the Singleton bound

Journal of Algebra and Its Applications ◽

10.1142/s0219498820501510 ◽

2019 ◽

Vol 19 (08) ◽

pp. 2050151 ◽

Cited By ~ 5

Author(s):

Hai Q. Dinh ◽

Xiaoqiang Wang ◽

Jirakom Sirisrisakulchai

Keyword(s):

Finite Field ◽

Cyclic Codes ◽

Maximum Distance ◽

Constacyclic Codes ◽

Singleton Bound ◽

Maximum Distance Separable

Let [Formula: see text] be the finite field of order [Formula: see text], where [Formula: see text] is a power of odd prime [Formula: see text]. Assume that [Formula: see text], [Formula: see text] are nonzero elements of the finite field [Formula: see text] such that [Formula: see text]. In this paper, we determine the [Formula: see text]-distance of [Formula: see text]-constacyclic codes with generator polynomials [Formula: see text] of length [Formula: see text], where [Formula: see text] and [Formula: see text]. As an application, all maximum distance separable (MDS) [Formula: see text]-symbol constacyclic codes of length [Formula: see text] over [Formula: see text] are established. Among other results, we construct several classes of new MDS symbol-pair codes with minimum symbol-pair distance six or seven by using repeated-root cyclic codes of length [Formula: see text] and [Formula: see text], respectively, where [Formula: see text] is an odd prime.

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Construction of new quantum MDS codes derived from constacyclic codes

International Journal of Quantum Information ◽

10.1142/s0219749917500083 ◽

2017 ◽

Vol 15 (01) ◽

pp. 1750008 ◽

Cited By ~ 2

Author(s):

Divya Taneja ◽

Manish Gupta ◽

Rajesh Narula ◽

Jaskaran Bhullar

Keyword(s):

Minimum Distance ◽

Maximum Distance ◽

Mds Codes ◽

Constacyclic Codes ◽

Maximum Distance Separable ◽

Work Done ◽

Quantum Mds Codes

Obtaining quantum maximum distance separable (MDS) codes from dual containing classical constacyclic codes using Hermitian construction have paved a path to undertake the challenges related to such constructions. Using the same technique, some new parameters of quantum MDS codes have been constructed here. One set of parameters obtained in this paper has achieved much larger distance than work done earlier. The remaining constructed parameters of quantum MDS codes have large minimum distance and were not explored yet.

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