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

Yıl 2021, Cilt: 8 Sayı: 1, 1 - 8, 15.01.2021

Yasemin Cengellenmis Nuh Aydin Abdullah Dertli

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

Öz

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.

Anahtar Kelimeler

DNA codes Skew codes Reversibility

Kaynakça

  • [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.

Yıl 2021, Cilt: 8 Sayı: 1, 1 - 8, 15.01.2021

Yasemin Cengellenmis Nuh Aydin Abdullah Dertli

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

Öz

Kaynakça

  • [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.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Yasemin Cengellenmis Bu kişi benim 0000-0002-8133-9836

Nuh Aydin Bu kişi benim 0000-0002-5618-2427

Abdullah Dertli 0000-0001-8687-032X

Yayımlanma Tarihi 15 Ocak 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 8 Sayı: 1

Kaynak Göster

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. Ocak 2021;8(1):1-8. doi:10.13069/jacodesmath.864902
Chicago Cengellenmis, Yasemin, Nuh Aydin, ve Abdullah Dertli. “Reversible DNA Codes from Skew Cyclic Codes over a Ring of Order 256”. Journal of Algebra Combinatorics Discrete Structures and Applications 8, sy. 1 (Ocak 2021): 1-8. https://doi.org/10.13069/jacodesmath.864902.
EndNote Cengellenmis Y, Aydin N, Dertli A (01 Ocak 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, ve A. Dertli, “Reversible DNA codes from skew cyclic codes over a ring of order 256”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 8, sy. 1, ss. 1–8, 2021, doi: 10.13069/jacodesmath.864902.
ISNAD Cengellenmis, Yasemin vd. “Reversible DNA Codes from Skew Cyclic Codes over a Ring of Order 256”. Journal of Algebra Combinatorics Discrete Structures and Applications 8/1 (Ocak 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 vd. “Reversible DNA Codes from Skew Cyclic Codes over a Ring of Order 256”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 8, sy. 1, 2021, ss. 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

Cyclic DNA codes over the ring $\mathbb{Z}_4+u\mathbb{Z}_4+u^2\mathbb{Z}_4$
Journal of Algebra Combinatorics Discrete Structures and Applications
Karthick GOWTHAMAN
https://doi.org/10.13069/jacodesmath.1000959