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Open AccessArticle

New DNA Codes from Cyclic Codes over Mixed Alphabets

1
Department of Mathematics, Kent State University, Warren, OH 44483, USA
2
Department of Mathematics, Indian Institute of Technology Patna, Patna 801103, India
3
Centre of Excellence in Econometrics, Faculty of Economics, Chiang Mai University, Chiang Mai 50200, Thailand
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(11), 1977; https://doi.org/10.3390/math8111977
Received: 10 October 2020 / Revised: 30 October 2020 / Accepted: 2 November 2020 / Published: 6 November 2020
(This article belongs to the Special Issue Algebra and Its Applications)
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]xα1×R[x]xβ1×S[x]xγ1. 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. View Full-Text
Keywords: cyclic codes; reversible codes; reversible-complement codes; cyclic DNA codes cyclic codes; reversible codes; reversible-complement codes; cyclic DNA codes
MDPI and ACS Style

Dinh, H.Q.; Pathak, S.; Upadhyay, A.K.; Yamaka, W. New DNA Codes from Cyclic Codes over Mixed Alphabets. Mathematics 2020, 8, 1977. https://doi.org/10.3390/math8111977

AMA Style

Dinh HQ, Pathak S, Upadhyay AK, Yamaka W. New DNA Codes from Cyclic Codes over Mixed Alphabets. Mathematics. 2020; 8(11):1977. https://doi.org/10.3390/math8111977

Chicago/Turabian Style

Dinh, Hai Q.; Pathak, Sachin; Upadhyay, Ashish K.; Yamaka, Woraphon. 2020. "New DNA Codes from Cyclic Codes over Mixed Alphabets" Mathematics 8, no. 11: 1977. https://doi.org/10.3390/math8111977

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