DNA CODES FROM REVERSIBLE GROUP CODES BY A VIRUS OPTIMISATION ALGORITHM

Year 2023, , 27 - 43, 15.10.2023

Adrian Korban , Serap Şahinkaya , Deniz Üstün

https://doi.org/10.33773/jum.1335373

Cited By: 1

Abstract

In this paper, we employ group rings and some known results on group codes to study reversible group DNA codes. We define and study reversible cyclic DNA codes from a group ring point of view and we also introduce the notion for self-reciprocal group ring elements. Moreover, we search for reversible group DNA codes with the use of a virus optimisation algorithm. We obtain many good DNA codes that satisfy the Hamming distance, the reverse, the reverse-complement and the fixed GC-content constraints.

Keywords

DNA codes, reversible codes, group codes

Supporting Institution

TÜBİTAK

Project Number

1059B192000947

Thanks

Serap Sahinkaya would like to thank TUBITAK for the financial support while writing this paper (Grant No:1059B192000947)

References

• L. Adleman, Molecular computation of the solutions to combinatorial problems, Science, Vol. 266, pp. 1021{1024 (1994).
• K.G. Benerjee, S. Deb, M.K. Gupta, On conict free DNA codes, Cryptogr. Commun. Vol.13,pp.143{171 (2021). https://doi.org/10.1007/s12095-020-00459-7. DNA CODES 43
• W. Bosma, J. Cannon, C. Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput., Vol. 24, pp. 235-265 (1997).
• Y. Cengellenmis, A. Dertli, S.T. Dougherty, A. Korban, S. Sahinkaya, D. Ustun, Reversible G-Codes over the Ring Fj;k with Applications to DNA Codes, Advances in MAtehematics of Communication, (2023) Doi: 10.3934/amc.2021056.
• Cuevas, J. R., H. J. Wang, Y. C. Lai, Y. C. Liang, Virus Optimization Algorithm: A Novel Metaheuristic for Solving Continuous Optimization Problems, The 10th Asia Paci_c Industrial Engineering Management System Conference, pp.2166{2174 (2009).
• S.T. Dougherty, J. Gildea, R. Taylor, A. Tylshchak, Group rings, G-codes and constructions of self-dual and formally self-dual codes, Designs, Codes and Cryptography, Vol. 86, pp.2115-2138 (2018).
• P. Gaborit, O. D. King, Linear Constructions for DNA Codes, Theoretical Computer Science, Vol.334, pp.99-113 (2005).
• F. Gursoy, E. S. Oztas, I. Siap, Reversible DNA codes over F16 + uF16 + vF16 + uvF16, Adv. Math. Commun., Vol.11, pp.307-312 (2017).
• H. J. Kim, W-H. Choi, Y. Lee, Designing DNA codes from reversible self-dual codes over GF(4), Discrete Mathematics, Vol.344, (2021).
• A. Korban, S. Sahinkaya, D. Ustun, An Application of the Virus Optimization Algorithm to the Problem of Finding Extremal Binary Self-Dual Codes, Advances in Matehematics of Communication, (2022) Doi: 10.3934/amc.2022098.
• A. Korban, S.Sahinkaya, D. Ustun, DNA Codes from Reversible Group Codes by a Virus Optimisation Algorithm, Available at https://sites.google.com/view/adriankorban/generator-matrices.
• A. Marathe, A.E. Condon, R.M. Corn, On combinatorial DNA word design, J. Comput. Biol., Vol.8, pp.201-220 (2001).
• J.L. Massey, Reversible codes, Information and Control, Vol.7, pp.369-380 (1964).
• W. Song, K. Cai, M. Zhang, C. Yuen, Codes with run-length and GC-content constraints for DNA-based data storage, IEEE Commun. Lett. Vol.22, No.10, pp.2004{2007 (2018). https://doi.org/10.1109/LCOMM.2018.2866566.
• E. S. Oztas, B. Yildiz, I. Siap, A novel approach for constructing reversible codes and appli- cations to DNA codes over the ring F2[u]=(u2k1), Finite Fields and Their Applications, Vol.46, pp. 217-234 (2017).
• E.S. Oztas, I. Siap, Lifted Polynomials over F16 and Their Applications to DNA Codes, Filomat, Vol.27, pp.459-466, (2013).
• X. Zhu, C. Sun, W. Liu, W. Wu, Research on the counting problem based on linear constructions for DNA coding, In: Proceedings Computational Intelligence and Bioinformatics, pp. 294{302 (2006).