On the DNA codes

Abdullah DERTLI; Yasemin CENGELLENMIS

doi:10.26637/mjm1104/001

Abstract

In this paper, by using three different methods, the DNA codes are obtained from some codes over a family of the rings $D_{i}=D_{1}\left[ w_{2},...,w_{i}\right]/\left\langle w_{i}^{2}-w_{i},w_{i}w_{j}-w_{j}w_{i}\right\rangle$ , where $i=2,...,r,j=1,2,...r$ and $D_{1}=F_{2}+uF_{2}+w_{1}(F_{2}+uF_{2}),$ $u^{2}=0,$ $w_{1}^{2}=w_{1},uw_{1}=w_{1}u, F_{2}=\{0,1\}$ .

Keywords:

DNA codes, skew codes, reversibility

Mathematics Subject Classification:

94B05, 95B60

Authors Imprint References Funding Related Articles Downloads

Abdullah DERTLI Department of Mathematics, Ondokuz Mayıs University Samsun, Turkey.
Yasemin CENGELLENMIS Department of Mathematics, Trakya University, Edirne, Turkey. https://orcid.org/0000-0002-8133-9836

Pages: 332-343
Date Published: 01-10-2023
Vol. 11 No. 04 (2023): Malaya Journal of Matematik (MJM)

L. A DLEMAN , Molecular computation of the solutions to combinatorial problems, Science, 266(1994), 1021–1024. DOI: https://doi.org/10.1126/science.7973651

Y. C ENGELLENMIS AND A. D ERTLI , On the cyclic DNA codes over the finite ring, Acta Universitatis Apulensis, 58(2019), 1–11. DOI: https://doi.org/10.17114/j.aua.2019.58.01

K. G UENDA AND T.A. G ULLIVER , Construction of cyclic codes over F 2 + uF 2 for DNA computing, Applicable Algebra in Engineering, Communication and Computing, 24(2013), 445-459. DOI: https://doi.org/10.1007/s00200-013-0188-x

F. G URSOY , E. S. O ZTAS AND I. S IAP ], R EVERSIBLE DNA CODES OVER F 16 + uF 16 + vF 16 + uvF 16 , arXiv:1703.10189v1, 2017.

F. G URSOY , E. S. O ZTAS AND A. O ZKAN , R EVERSIBLE DNA CODES OVER A FAMILY OF NON - CHAIN RING , arXiv:1711.02385v1, 2017.

F. G URSOY , E. S. O ZTAS AND I. S IAP , R EVERSIBLE DNA CODES USING SKEW POLYNOMIAL RINGS , Applicable Algebra in Engineering, Communication and Computing, 28(2017), 311–320. DOI: https://doi.org/10.1007/s00200-017-0325-z

T. H EAD , F ORMAL LANGUAGE THEORY AND DNA: AN ANALYSIS OF THE GENERATIVE CAPACITY OF SPECIFIC RECOMBINANT BEHAVIORS , Bulletin of mathematical biology, 49(1987), 737–759. DOI: https://doi.org/10.1016/S0092-8240(87)90018-8

J. L IANG AND W. L IQI , O N CYCLIC DNA CODES OVER F 2 +uF 2 , Journal of Applied Mathematics and Computing, 51(2016), 81–91. DOI: https://doi.org/10.1007/s12190-015-0892-8

B. Y ILDIZ AND I. S IAP , C YCLIC CODES OVER F 2 [u]/ < u 4 −1 > AND APPLICATIONS TO DNA CODES ., Computers Mathematics with Applications, 63(2012), 1169–1176. DOI: https://doi.org/10.1016/j.camwa.2011.12.029

S. Z HU AND X. C HEN , C YCLIC DNA CODES OVER F 2 + uF 2 + vF 2 + uvF 2 AND THEIR APPLICATIONS , Journal of Applied Mathematics and Computation, 55(2017), 479–493. DOI: https://doi.org/10.1007/s12190-016-1046-3