On the Structure of Cyclic Codes Over $\mathbb{F}_{q}{RS}$  and Applications in Quantum and LCD Codes Constructions

Dinh, Hai Q.; Bag, Tushar; Upadhyay, Ashish Kumar; Bandi, Ramakrishna; Chinnakum, Warattaya

doi:10.1109/access.2020.2966542

Cited by 29 publications

(10 citation statements)

References 43 publications

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“…They were all obtained using the same method as the codes in the previous table. Codes with the same parameters listed in Table 6 were found using more complex and indirect methods detailed in [21], [22], [23] , [24], [25], [26]. These constructions usually involve considering an extension ring S of a ground ring or field R, constructing a code over the extension ring, then coming back to R using some sort of Gray map.…”

Section: Quantum Codesmentioning

confidence: 99%

Good Classical and Quantum Codes from Multi-Twisted Codes

Aydın¹,

Guidotti²,

Liu³

2020

Preprint

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Multi-twisted (MT) codes were introduced as a generalization of quasi-twisted (QT) codes. QT codes have been known to contain many good codes. In this work, we show that codes with good parameters and desirable properties can be obtained from MT codes. These include best known and optimal classical codes with additional properties such as reversibility and self-duality, and new and best known non-binary quantum codes obtained from special cases MT codes. Often times best known quantum codes in the literature are obtained indirectly by considering extension rings. Our constructions have the advantage that we obtain these codes by more direct and simpler methods. Additionally, we found theoretical results about binomials over finite fields that are useful in our search.

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Section: Quantum Codesmentioning

confidence: 99%

Good Classical and Quantum Codes from Multi-Twisted Codes

Aydın¹,

Guidotti²,

Liu³

2020

Preprint

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“…Shi et al studied LCD codes over Galois rings, and obtained some classes of asymptotically good LCD codes [30]. Dinh et al studied the construction of LCD codes from F q × (F q + uF q ) × (F q + uF q + vF q + uvF q )additive cyclic codes [31], where u 2 = 1, v 2 = 1, uv = vu.…”

Section: Introductionmentioning

confidence: 99%

On Z₂Z₂[u³]-Additive Cyclic and Complementary Dual Codes

2021

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Aydogdu et al. studied the standard forms of generator and parity-check matrices of Z 2 Z 2 [u 3 ]-additive codes, and presented generators of Z 2 Z 2 [u 3 ]-additive cyclic codes (Finite Fields Appl. 48: 241-260, 2017). In this paper, we investigate some other useful properties of Z 2 Z 2 [u 3 ]-additive codes, including asymptotically good Z 2 Z 2 [u 3 ]-additive cyclic codes and Z 2 Z 2 [u 3 ]-additive complementary dual codes. The present paper can be viewed as a necessary complementary part of Aydogdu's work.

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“…After that, many good QECCs have been constructed by using the cyclic and constacyclic codes over finite fields. Working over finite rings, researchers have constructed QECCs with better parameters [1]- [3], [5], [6], [8], [21]- [23], [25], [26], [28], [32], [33], [36]. Very recently, Bag et al [7] studied the dual containing property of constacyclic and skew constacyclic codes over finite rings and constructed new non binary QECCs from their studies.…”

Section: Introductionmentioning

confidence: 99%

Quantum Codes Obtained From Constacyclic Codes Over a Family of Finite Rings F_p[u₁, u₂, …, u_s]

et al. 2020

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In this paper, we construct some MDS quantum error-correcting codes (QECCs) from classes of constacyclic codes over R s = F p + u 1 F p + • • • + u s F p , u 2 i = u i , u i u j = u j u i = 0, for odd prime p and i, j = 1, 2,. .. , s, i = j. Many QECCs with improved parameters than the existing ones in some of the earlier papers are provided. We present a set of idempotent generators of the ring R s , and using that we define linear codes, determine all units, and study constacyclic codes over this ring. Among others, we study dual containing constacyclic codes over R s and construct (non-binary) QECCs. An algorithm to construct QECCs from dual containing constacyclic codes over R s is obtained that can provide many quantum codes. INDEX TERMS Cyclic codes, negacyclic codes, constacyclic codes, quantum codes.

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On the Structure of Cyclic Codes Over $\mathbb{F}_{q}{RS}$ and Applications in Quantum and LCD Codes Constructions

Cited by 29 publications

References 43 publications

Good Classical and Quantum Codes from Multi-Twisted Codes

Good Classical and Quantum Codes from Multi-Twisted Codes

On Z₂Z₂[u³]-Additive Cyclic and Complementary Dual Codes

Quantum Codes Obtained From Constacyclic Codes Over a Family of Finite Rings F_p[u₁, u₂, …, u_s]

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On the Structure of Cyclic Codes Over $\mathbb{F}_{q}{RS}$ and Applications in Quantum and LCD Codes Constructions

Cited by 29 publications

References 43 publications

Good Classical and Quantum Codes from Multi-Twisted Codes

Good Classical and Quantum Codes from Multi-Twisted Codes

On Z₂Z₂[u³]-Additive Cyclic and Complementary Dual Codes

Quantum Codes Obtained From Constacyclic Codes Over a Family of Finite Rings Fp[u₁, u₂, …, us]

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Product

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Quantum Codes Obtained From Constacyclic Codes Over a Family of Finite Rings F_p[u₁, u₂, …, u_s]