Araştırma Makalesi
Yıl 2023,
Cilt: 6 Sayı: 3-Supplement, 27 - 43, 15.10.2023
Öz
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.
Anahtar Kelimeler
Destekleyen Kurum
TÜBİTAK
Proje Numarası
1059B192000947
Teşekkür
Serap Sahinkaya would like to thank TUBITAK for the financial support while writing this paper (Grant No:1059B192000947)
Kaynakça
- 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).
Yıl 2023,
Cilt: 6 Sayı: 3-Supplement, 27 - 43, 15.10.2023
Öz
Proje Numarası
1059B192000947
Kaynakça
- 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).
Toplam 17 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Cebir ve Sayı Teorisi |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Proje Numarası | 1059B192000947 |
| Yayımlanma Tarihi | 15 Ekim 2023 |
| Gönderilme Tarihi | 31 Temmuz 2023 |
| Kabul Tarihi | 3 Ekim 2023 |
| Yayımlandığı Sayı | Yıl 2023 Cilt: 6 Sayı: 3-Supplement |
