Reversible cyclic codes over some finite rings and their application to DNA codes

Prakash, Om; Patel, Shikha; Yadav, Shikha

doi:10.1007/s40314-021-01635-y

Cited by 7 publications

(4 citation statements)

References 7 publications

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“…Type of Code Gray Image DNA Code [14] g 2 g 3 , vg 2 g 3 , v 2 g 2 g 3 (15, 13, 2) (45, 4 39 , 2) (45, 4 26 , 2) g 2 g 3 g 6 , vg 2 g 3 g 6 , v 2 g 2 g 3 g 6 (15,11,4) (45, 4 33 , 4) (45, 4 24 , 3) g 4 g 8 g 9 , vg 4 g 8 g 9 , v 2 g 4 g 8 g 9 (15,9,5) (45, 4 27 , 5) (45, 4 18 , 5) g 2 g 3 g 5 g 6 g 7 , vg 2 g 3 g 5 g 6 g 7 , v 2 g 2 g 3 g 5 g 6 g 7…”

Section: Codementioning

confidence: 99%

“…(15, 7, 7) (45, 4 21 , 7) (45, 4 14 , 7) g 2 g 3 g 4 g 5 g 6 g 7 g 9 , vg 2 g 3 g 4 g 5 g 6 g 7 g 9 , v 2 g 2 g 3 g 4 g 5 g 6 g 7 g 9 (15,3,9) (45, 4 9 , 9) (45, 4 6 , 9)…”

Section: Codementioning

confidence: 99%

“…Within the class of linear codes, cyclic codes are the pivotal and the most studied codes due to their theoretical richness and practical implementation. Recently, many authors [7][8][9][10][11][12][13] constructed DNA codes using cyclic codes over rings. For instance, Bayram et al [7] and Yildiz and Siap [13] explored DNA codes over the rings F 4 + vF 4 , v 2 = v and F 2 [v]/ v 4 − 1 , respectively.…”

Section: Introductionmentioning

confidence: 99%

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DNA Code from Cyclic and Skew Cyclic Codes over F4[v]/⟨v3⟩

Prakash

Singh

Verma

et al. 2023

Entropy

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The main motivation of this work is to study and obtain some reversible and DNA codes of length n with better parameters. Here, we first investigate the structure of cyclic and skew cyclic codes over the chain ring R:=F4[v]/⟨v3⟩. We show an association between the codons and the elements of R using a Gray map. Under this Gray map, we study reversible and DNA codes of length n. Finally, several new DNA codes are obtained that have improved parameters than previously known codes. We also determine the Hamming and the Edit distances of these codes.

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Section: Codementioning

confidence: 99%

“…(15, 7, 7) (45, 4 21 , 7) (45, 4 14 , 7) g 2 g 3 g 4 g 5 g 6 g 7 g 9 , vg 2 g 3 g 4 g 5 g 6 g 7 g 9 , v 2 g 2 g 3 g 4 g 5 g 6 g 7 g 9 (15,3,9) (45, 4 9 , 9) (45, 4 6 , 9)…”

Section: Codementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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DNA Code from Cyclic and Skew Cyclic Codes over F4[v]/⟨v3⟩

Prakash

Singh

Verma

et al. 2023

Entropy

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“…Cyclic codes over fnite chain rings with length coprime to the characteristic of residue feld have been investigated in references [2,16,22]. Islam and Prakash have established a unique set of generators for cyclic codes over Z p k in reference [4] and for cyclic codes over F q + uF q , u 2 � 0 in reference [5]. A. Sharma and T. Sidana have studied cyclic codes of p s length over fnite chain rings in reference [15], thereby extending the results of Kiah et al on cyclic codes over Galois rings [14].…”

Section: Introductionmentioning

confidence: 99%

MDS and MHDR Cyclic Codes over Finite Chain Rings

Dalal,

Dutt,

Sehmi

2024

Journal of Mathematics

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This work establishes a unique set of generators for a cyclic code over a finite chain ring. Towards this, we first determine the minimal spanning set and rank of the code. Furthermore, sufficient as well as necessary conditions for a cyclic code to be an MDS code and for a cyclic code to be an MHDR code are obtained. Finally, to support our results, some examples of optimal cyclic codes are presented.

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On reversible DNA codes over the ring $${\mathbb {Z}}_4[u,v]/\langle u^2-2,uv-2,v^2,2u,2v\rangle$$ based on the deletion distance

Dinh,

Ashraf,

Rehman

et al. 2024

AAECC

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Let $${\mathfrak {R}}= {\mathbb {Z}}_4[u,v]/\langle u^2-2,uv-2,v^2,2u,2v\rangle$$ R = Z 4 [ u , v ] / ⟨ u 2 - 2 , u v - 2 , v 2 , 2 u , 2 v ⟩ be a ring, where $${\mathbb {Z}}_{4}$$ Z 4 is a ring of integers modulo 4. This ring $${\mathfrak {R}}$$ R is a local non-chain ring of characteristic 4. The main objective of this article is to construct reversible cyclic codes of odd length n over the ring $${\mathfrak {R}}.$$ R . Employing these reversible cyclic codes, we obtain reversible cyclic DNA codes of length n, based on the deletion distance over the ring $${\mathfrak {R}}.$$ R . We also construct a bijection $$\Gamma$$ Γ between the elements of the ring $${\mathfrak {R}}$$ R and $$S_{D_{16}}.$$ S D 16 . As an application of $$\Gamma ,$$ Γ , the reversibility problem which occurs in DNA k-bases has been solved. Moreover, we introduce a Gray map $$\Psi _{\hom }:{\mathfrak {R}}^{n}\rightarrow {\mathbb {F}}_{2}^{8n}$$ Ψ hom : R n → F 2 8 n with respect to homogeneous weight $$w_{\hom }$$ w hom over the ring $${\mathfrak {R}}$$ R . Further, we discuss the GC-content of DNA cyclic codes and their deletion distance. Moreover, we provide some examples of reversible DNA cyclic codes.

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Reversible cyclic codes over some finite rings and their application to DNA codes

Cited by 7 publications

References 7 publications

DNA Code from Cyclic and Skew Cyclic Codes over F4[v]/⟨v3⟩

DNA Code from Cyclic and Skew Cyclic Codes over F4[v]/⟨v3⟩

MDS and MHDR Cyclic Codes over Finite Chain Rings

On reversible DNA codes over the ring $${\mathbb {Z}}_4[u,v]/\langle u^2-2,uv-2,v^2,2u,2v\rangle$$ based on the deletion distance

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