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DNA CODES FROM REVERSIBLE GROUP CODES BY A VIRUS OPTIMISATION ALGORITHM

Year 2023, Volume: 6 Issue: 3-Supplement, 27 - 43, 15.10.2023
https://doi.org/10.33773/jum.1335373

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.

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).
Year 2023, Volume: 6 Issue: 3-Supplement, 27 - 43, 15.10.2023
https://doi.org/10.33773/jum.1335373

Abstract

Project Number

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).
There are 17 citations in total.

Details

Primary Language English
Subjects Algebra and Number Theory
Journal Section Research Article
Authors

Adrian Korban 0000-0001-5206-6480

Serap Şahinkaya 0000-0002-2084-6260

Deniz Üstün 0000-0002-5229-4018

Project Number 1059B192000947
Publication Date October 15, 2023
Submission Date July 31, 2023
Acceptance Date October 3, 2023
Published in Issue Year 2023 Volume: 6 Issue: 3-Supplement

Cite

APA Korban, A., Şahinkaya, S., & Üstün, D. (2023). DNA CODES FROM REVERSIBLE GROUP CODES BY A VIRUS OPTIMISATION ALGORITHM. Journal of Universal Mathematics, 6(3-Supplement), 27-43. https://doi.org/10.33773/jum.1335373
AMA Korban A, Şahinkaya S, Üstün D. DNA CODES FROM REVERSIBLE GROUP CODES BY A VIRUS OPTIMISATION ALGORITHM. JUM. October 2023;6(3-Supplement):27-43. doi:10.33773/jum.1335373
Chicago Korban, Adrian, Serap Şahinkaya, and Deniz Üstün. “DNA CODES FROM REVERSIBLE GROUP CODES BY A VIRUS OPTIMISATION ALGORITHM”. Journal of Universal Mathematics 6, no. 3-Supplement (October 2023): 27-43. https://doi.org/10.33773/jum.1335373.
EndNote Korban A, Şahinkaya S, Üstün D (October 1, 2023) DNA CODES FROM REVERSIBLE GROUP CODES BY A VIRUS OPTIMISATION ALGORITHM. Journal of Universal Mathematics 6 3-Supplement 27–43.
IEEE A. Korban, S. Şahinkaya, and D. Üstün, “DNA CODES FROM REVERSIBLE GROUP CODES BY A VIRUS OPTIMISATION ALGORITHM”, JUM, vol. 6, no. 3-Supplement, pp. 27–43, 2023, doi: 10.33773/jum.1335373.
ISNAD Korban, Adrian et al. “DNA CODES FROM REVERSIBLE GROUP CODES BY A VIRUS OPTIMISATION ALGORITHM”. Journal of Universal Mathematics 6/3-Supplement (October 2023), 27-43. https://doi.org/10.33773/jum.1335373.
JAMA Korban A, Şahinkaya S, Üstün D. DNA CODES FROM REVERSIBLE GROUP CODES BY A VIRUS OPTIMISATION ALGORITHM. JUM. 2023;6:27–43.
MLA Korban, Adrian et al. “DNA CODES FROM REVERSIBLE GROUP CODES BY A VIRUS OPTIMISATION ALGORITHM”. Journal of Universal Mathematics, vol. 6, no. 3-Supplement, 2023, pp. 27-43, doi:10.33773/jum.1335373.
Vancouver Korban A, Şahinkaya S, Üstün D. DNA CODES FROM REVERSIBLE GROUP CODES BY A VIRUS OPTIMISATION ALGORITHM. JUM. 2023;6(3-Supplement):27-43.