scholarly journals Cyclic DNA codes over the ring $\mathbb{Z}_4+u\mathbb{Z}_4+u^2\mathbb{Z}_4$

2021 ◽  
pp. 219-231
Author(s):  
Karthick GOWTHAMAN ◽  
Somi GUPTA ◽  
Cruz MOHAN ◽  
Kenza GUENDA ◽  
Durairajan CHİNNAPİLLAİ
Keyword(s):  
Dna Codes ◽  
Cyclic Dna Codes

scholarly journals New DNA Codes from Cyclic Codes over Mixed Alphabets

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1977
Author(s):  
Hai Q. Dinh ◽  
Sachin Pathak ◽  
Ashish Kumar Upadhyay ◽  
Woraphon Yamaka
Keyword(s):  
Cyclic Codes ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Block Length ◽  
Dna Codes ◽  
Reverse Complement ◽  
Gray Maps ◽  
Cyclic Dna Codes ◽  
One To One ◽  
Necessary And Sufficient

Let R=F4+uF4,withu2=u and S=F4+uF4+vF4,withu2=u,v2=v,uv=vu=0. In this paper, we study F4RS-cyclic codes of block length (α,β,γ) and construct cyclic DNA codes from them. F4RS-cyclic codes can be viewed as S[x]-submodules of Fq[x]⟨xα−1⟩×R[x]⟨xβ−1⟩×S[x]⟨xγ−1⟩. We discuss their generator polynomials as well as the structure of separable codes. Using the structure of separable codes, we study cyclic DNA codes. By using Gray maps ψ1 from R to F42 and ψ2 from S to F43, we give a one-to-one correspondence between DNA codons of the alphabets {A,T,G,C}2,{A,T,G,C}3 and the elements of R,S, respectively. Then we discuss necessary and sufficient conditions of cyclic codes over F4, R, S and F4RS to be reversible and reverse-complement. As applications, we provide examples of new cyclic DNA codes constructed by our results.

scholarly journals Construction of Cyclic DNA Codes Over the Ring Z4 + vZ4

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 111200-111207 ◽  
Author(s):  
Jie Liu ◽  
Hualu Liu
Keyword(s):  
Dna Codes ◽  
Cyclic Dna Codes

scholarly journals On cyclic DNA codes over the rings Z4 + wZ4 and Z4 + wZ4 + vZ4 + wvZ4

BIOMATH ◽  
2017 ◽  
Vol 6 (2) ◽  
pp. 1712167 ◽  
Author(s):  
Abdullah Dertli ◽  
Yasemin Cengellenmis
Keyword(s):  
Cyclic Codes ◽  
Finite Ring ◽  
Finite Rings ◽  
Binary Images ◽  
Dna Codes ◽  
Reverse Complement ◽  
Skew Cyclic Codes ◽  
Cyclic Dna Codes

The structures of cyclic DNA codes of odd length over the finite rings R = Z4 + wZ4, w^2 = 2 and S = Z4 + wZ4 + vZ4 + wvZ4; w^2 = 2; v^2 =v; wv = vw are studied. The links between the elements of the rings R, S and 16 and 256 codons are established, respectively. The cyclic codes of odd length over the finite ring R satisfy reverse complement constraint and the cyclic codes of odd length over the finite ring S satisfy reverse constraint and reverse complement constraint are studied. The binary images of the cyclic DNA codes over the finite rings R and S are determined. Moreover, a family of DNA skew cyclic codes over R is constructed, its property of being reverse complement is studied.

DNA cyclic codes over the ring 𝔽2[u,v]/〈u2 − 1,v3 − v,uv − vu〉

2018 ◽  
Vol 11 (03) ◽  
pp. 1850042 ◽  
Author(s):  
Hai Q. Dinh ◽  
Abhay Kumar Singh ◽  
Sukhamoy Pattanayak ◽  
Songsak Sriboonchitta
Keyword(s):  
Cyclic Code ◽  
Cyclic Codes ◽  
Sufficient Conditions ◽  
Gray Map ◽  
Arbitrary Length ◽  
Binary Images ◽  
Dna Codes ◽  
Cyclic Dna Codes ◽  
Living Organisms ◽  
Necessary And Sufficient

In this paper, our main objective is to find out the necessary and sufficient conditions for a cyclic code of arbitrary length over the ring of four elements [Formula: see text] [Formula: see text] to be a reversible cyclic code. We also obtain the structure of cyclic DNA codes of odd length over the ring [Formula: see text], which plays an important role in Computational Biology. Furthermore, we establish a direct link between the elements of ring [Formula: see text] and 64 codons used in the amino acids of living organisms by introducing a Gray map from [Formula: see text] to [Formula: see text]. Among others, binary images of cyclic codes over [Formula: see text] are also investigated. As applications, some cyclic DNA codes over [Formula: see text] using the Gray map are provided.

On cyclic DNA codes

2013 ◽  
Author(s):  
K. Guenda ◽  
T. Aaron Gulliver ◽  
Patrick Sole
Keyword(s):  
Dna Codes ◽  
Cyclic Dna Codes
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