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Reversible DNA codes from skew cyclic codes over a ring of order 256

Year 2021, Volume: 8 Issue: 1, 1 - 8, 15.01.2021

Yasemin Cengellenmis Nuh Aydin Abdullah Dertli

https://doi.org/10.13069/jacodesmath.864902
Cited By: 1

Abstract

We introduce skew cyclic codes over the finite ring $\R$, where $u^{2}=0,v^{2}=v,w^{2}=w,uv=vu,uw=wu,vw=wv$ and use them to construct reversible DNA codes. The 4-mers are matched with the elements of this ring. The reversibility problem for DNA 4-bases is solved and some examples are provided.

Keywords

DNA codes Skew codes Reversibility

References

  • [1] T. Abualrub, A. Ghrayeb, X. N. Zeng, Construction of cyclic codes over GF(4) for DNA computing, J. Frankl. Inst. 343(4-5) (2006) 448–457.
  • [2] L. Adleman, Molecular computation of the solutions to combinatorial problems, Science 266 (1994) 1021–1024.
  • [3] L. Adleman, P. W. K. Rothemund, S. Roweis, E. Winfree, On applying molecular computation to the data encryption standard, J. Comp. Biology 6(1) (1999) 53–63.
  • [4] N. Bennenni, K. Guenda, S. Mesnager, DNA cyclic codes over rings, Advances in Mathematics of Communications 11(1) (2017) 83–98.
  • [5] D. Boneh, C. Dunworth, R. Lipton, Breaking DES using molecular computer, Princeton CS Tech- Report, Number CS-TR-489-95 (1995).
  • [6] Y. Cengellenmis, A. Dertli, On the cyclic DNA codes over the finite ring, Acta Universitatis Apulensis 58 (2019) 1–11.
  • [7] A. Dertli, Y. Cengellenmis, On cyclic DNA codes over the rings Z4+wZ4 and Z4+wZ4+vZ4+wvZ4, Biomath 6(2) (2017) 1712167.
  • [8] P. Gaborit, H. King, Linear constructions for DNA codes, Theor. Comput. Sci. 334(1âAS3) (2005) 99–113.
  • [9] K. Guenda, T. A. Gulliver, Construction of cyclic codes over F2 +uF2 for DNA computing, AAECC 24 (2013) 445–459.
  • [10] F. Gursoy, E. S. Oztas, I. Siap, Reversible DNA codes over F16 + uF16 + vF16 + uvF16, 11(2) 2017 307–312.
  • [11] F. Gursoy, E. S. Oztas, B. Yildiz, Reversible DNA codes over a family of non-chain ring, arXiv:1711.02385.
  • [12] F. Gursoy, E. S. Oztas, I. Siap, Reversible DNA codes using skew polynomial rings, Applicable Algebra in Engineering, Communication and Computing 28 (2017) 311–320.
  • [13] J. Liang, L. Wang, On cyclic DNA codes over F2 + uF2, J.Appl Math Comput. 52 (2016) 81–91.
  • [14] D. Limbachiya, B. Rao, G. K. Manish, The Art of DNA Strings: Sixteen Years of DNA Coding Theory, arXiv:1607.00266.
  • [15] Magma computer algebra system, online, http://magma.maths.usyd.edu.au/
  • [16] M. Mansuripur, P. K. Khulbe, S. M. Kuebler, J. W. Perry, M. S. Giridhar, N. Peyghambarian, Information storage and retrieval using macromolecules as storage media, in Optical Data Storage, OSA Technical Digest Series (Optical Society of America), paper TuC2 (2003).
  • [17] O. Milenkovic, N. Kashyap, On the design of codes for DNA computing, Lecture Notes in Computer Science 3969, Springer (2006) 100–119.
  • [18] E. S. Oztas, B. Yildiz and I. Siap, A novel approach for constructing reversible codes and applications to DNA codes over the ring F2[u]=(u2k 􀀀1), Finite Fields and Their Applications 46 (2017) 217–234.
  • [19] S. Pattanayak, A. K. Singh, Construction of cyclic DNA codes over the Ring Z4[u]= < u2 􀀀 1 > based on the deletion distance, arXiv:1603.04055.
  • [20] A. Sharma, B. Maheshanand, A class of skew-constacyclic codes over Z4+uZ4, International Journal of Information and Coding Theory 4(4) (2017) 289–303.
  • [21] I. Siap, T. Abualrub, A. Ghrayeb, Cyclic DNA codes over the ring F2[u]=(u2 􀀀 1) based on the deletion distance, J. Frankl. Inst. 346 (2009) 731–740.
  • [22] B. Yildiz, I. Siap, Cyclic codes over F2[u]=(u4 􀀀 1) and applications to DNA codes, Comput. Math. Appl. 63 (2012) 1169–1176.
  • [23] S. Zhu, X. Chen, Cyclic DNA codes over F2+uF2+vF2+uvF2 and their applications, J. Appl.Math Comput. 55 (2017) 479–493.

Year 2021, Volume: 8 Issue: 1, 1 - 8, 15.01.2021

Yasemin Cengellenmis Nuh Aydin Abdullah Dertli

https://doi.org/10.13069/jacodesmath.864902
Cited By: 1

Abstract

References

  • [1] T. Abualrub, A. Ghrayeb, X. N. Zeng, Construction of cyclic codes over GF(4) for DNA computing, J. Frankl. Inst. 343(4-5) (2006) 448–457.
  • [2] L. Adleman, Molecular computation of the solutions to combinatorial problems, Science 266 (1994) 1021–1024.
  • [3] L. Adleman, P. W. K. Rothemund, S. Roweis, E. Winfree, On applying molecular computation to the data encryption standard, J. Comp. Biology 6(1) (1999) 53–63.
  • [4] N. Bennenni, K. Guenda, S. Mesnager, DNA cyclic codes over rings, Advances in Mathematics of Communications 11(1) (2017) 83–98.
  • [5] D. Boneh, C. Dunworth, R. Lipton, Breaking DES using molecular computer, Princeton CS Tech- Report, Number CS-TR-489-95 (1995).
  • [6] Y. Cengellenmis, A. Dertli, On the cyclic DNA codes over the finite ring, Acta Universitatis Apulensis 58 (2019) 1–11.
  • [7] A. Dertli, Y. Cengellenmis, On cyclic DNA codes over the rings Z4+wZ4 and Z4+wZ4+vZ4+wvZ4, Biomath 6(2) (2017) 1712167.
  • [8] P. Gaborit, H. King, Linear constructions for DNA codes, Theor. Comput. Sci. 334(1âAS3) (2005) 99–113.
  • [9] K. Guenda, T. A. Gulliver, Construction of cyclic codes over F2 +uF2 for DNA computing, AAECC 24 (2013) 445–459.
  • [10] F. Gursoy, E. S. Oztas, I. Siap, Reversible DNA codes over F16 + uF16 + vF16 + uvF16, 11(2) 2017 307–312.
  • [11] F. Gursoy, E. S. Oztas, B. Yildiz, Reversible DNA codes over a family of non-chain ring, arXiv:1711.02385.
  • [12] F. Gursoy, E. S. Oztas, I. Siap, Reversible DNA codes using skew polynomial rings, Applicable Algebra in Engineering, Communication and Computing 28 (2017) 311–320.
  • [13] J. Liang, L. Wang, On cyclic DNA codes over F2 + uF2, J.Appl Math Comput. 52 (2016) 81–91.
  • [14] D. Limbachiya, B. Rao, G. K. Manish, The Art of DNA Strings: Sixteen Years of DNA Coding Theory, arXiv:1607.00266.
  • [15] Magma computer algebra system, online, http://magma.maths.usyd.edu.au/
  • [16] M. Mansuripur, P. K. Khulbe, S. M. Kuebler, J. W. Perry, M. S. Giridhar, N. Peyghambarian, Information storage and retrieval using macromolecules as storage media, in Optical Data Storage, OSA Technical Digest Series (Optical Society of America), paper TuC2 (2003).
  • [17] O. Milenkovic, N. Kashyap, On the design of codes for DNA computing, Lecture Notes in Computer Science 3969, Springer (2006) 100–119.
  • [18] E. S. Oztas, B. Yildiz and I. Siap, A novel approach for constructing reversible codes and applications to DNA codes over the ring F2[u]=(u2k 􀀀1), Finite Fields and Their Applications 46 (2017) 217–234.
  • [19] S. Pattanayak, A. K. Singh, Construction of cyclic DNA codes over the Ring Z4[u]= < u2 􀀀 1 > based on the deletion distance, arXiv:1603.04055.
  • [20] A. Sharma, B. Maheshanand, A class of skew-constacyclic codes over Z4+uZ4, International Journal of Information and Coding Theory 4(4) (2017) 289–303.
  • [21] I. Siap, T. Abualrub, A. Ghrayeb, Cyclic DNA codes over the ring F2[u]=(u2 􀀀 1) based on the deletion distance, J. Frankl. Inst. 346 (2009) 731–740.
  • [22] B. Yildiz, I. Siap, Cyclic codes over F2[u]=(u4 􀀀 1) and applications to DNA codes, Comput. Math. Appl. 63 (2012) 1169–1176.
  • [23] S. Zhu, X. Chen, Cyclic DNA codes over F2+uF2+vF2+uvF2 and their applications, J. Appl.Math Comput. 55 (2017) 479–493.
There are 23 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Yasemin Cengellenmis This is me 0000-0002-8133-9836

Nuh Aydin This is me 0000-0002-5618-2427

Abdullah Dertli 0000-0001-8687-032X

Publication Date January 15, 2021
Published in Issue Year 2021 Volume: 8 Issue: 1

Cite

APA Cengellenmis, Y., Aydin, N., & Dertli, A. (2021). Reversible DNA codes from skew cyclic codes over a ring of order 256. Journal of Algebra Combinatorics Discrete Structures and Applications, 8(1), 1-8. https://doi.org/10.13069/jacodesmath.864902
AMA Cengellenmis Y, Aydin N, Dertli A. Reversible DNA codes from skew cyclic codes over a ring of order 256. Journal of Algebra Combinatorics Discrete Structures and Applications. January 2021;8(1):1-8. doi:10.13069/jacodesmath.864902
Chicago Cengellenmis, Yasemin, Nuh Aydin, and Abdullah Dertli. “Reversible DNA Codes from Skew Cyclic Codes over a Ring of Order 256”. Journal of Algebra Combinatorics Discrete Structures and Applications 8, no. 1 (January 2021): 1-8. https://doi.org/10.13069/jacodesmath.864902.
EndNote Cengellenmis Y, Aydin N, Dertli A (January 1, 2021) Reversible DNA codes from skew cyclic codes over a ring of order 256. Journal of Algebra Combinatorics Discrete Structures and Applications 8 1 1–8.
IEEE Y. Cengellenmis, N. Aydin, and A. Dertli, “Reversible DNA codes from skew cyclic codes over a ring of order 256”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 8, no. 1, pp. 1–8, 2021, doi: 10.13069/jacodesmath.864902.
ISNAD Cengellenmis, Yasemin et al. “Reversible DNA Codes from Skew Cyclic Codes over a Ring of Order 256”. Journal of Algebra Combinatorics Discrete Structures and Applications 8/1 (January 2021), 1-8. https://doi.org/10.13069/jacodesmath.864902.
JAMA Cengellenmis Y, Aydin N, Dertli A. Reversible DNA codes from skew cyclic codes over a ring of order 256. Journal of Algebra Combinatorics Discrete Structures and Applications. 2021;8:1–8.
MLA Cengellenmis, Yasemin et al. “Reversible DNA Codes from Skew Cyclic Codes over a Ring of Order 256”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 8, no. 1, 2021, pp. 1-8, doi:10.13069/jacodesmath.864902.
Vancouver Cengellenmis Y, Aydin N, Dertli A. Reversible DNA codes from skew cyclic codes over a ring of order 256. Journal of Algebra Combinatorics Discrete Structures and Applications. 2021;8(1):1-8.

Cited By

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