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Cyclic DNA codes over the ring $\mathbb{Z}_4+u\mathbb{Z}_4+u^2\mathbb{Z}_4$

Yıl 2021, Cilt: 8 Sayı: 3, 219 - 231, 15.09.2021
https://doi.org/10.13069/jacodesmath.1000959

Öz

In this work, we have investigated the one generator cyclic DNA codes with reverse and reverse complement constraints over the ring $R=\mathbb{Z}_4+u\mathbb{Z}_4+u^2\mathbb{Z}_4$ with $u^3=0$. Skew cyclic codes with reverse complement constraint are constructed over $R$. We have also determined a one-to-one correspondence between the elements of the ring $R$ and DNA codons satisfying the Watson-Crick complement. Finally, we have established some examples which satisfy the given constraints.

Kaynakça

  • [1] T. Abualrub, R. Oehmke, On the generators of Z4 cyclic codes of length 2e, IEEE Transactions on Information Theory 49 (2003) 2126–2133.
  • [2] T. Abualrub, I. Siap, Cyclic codes over the rings Z2 + uZ2 and Z2 + uZ2 + u2Z2, Des Codes Crypt 42 (2007) 273–287.
  • [3] T. Abualrub, I. Siap, Reversible cyclic codes over Z4, Australasian Journal of Combinatorics 38 (2007) 195–205.
  • [4] L. M. Adleman, Molecular computation of solutions to combinatorial problems, Science 266 (1994) 1021–1024.
  • [5] N. Bennenni, K. Guenda, S. Mesnager, New DNA cyclic codes over rings, Adv. Math. Comp. 11(1) (2017) 83–98.
  • [6] A. Bonnecaze, P. Udaya, Cyclic codes and self-dual codes over F2 + uF2, IEEE Transactions on Information Theory 45 (1999) 1250–1255.
  • [7] D. Boucher, W. Geiselmann, F. Ulmer, Skew cyclic codes, Applied Algebra in Engineering, Communication and Computing 18 (2007) 379–389.
  • [8] D. Boucher, F. Ulmer, Coding with skew polynomial rings, Journal of Symbolic Computation 44 (2009) 1644–1656.
  • [9] Y. Cengellenmis, N. Aydin, A. Dertli, Reversible DNA codes from skew cyclic codes over a ring of order 256, J. Algebra Comb. Discrete Appl. 8(1) (2021) 1–8.
  • [10] H. Q. Dinh, S. Pattanayak, A. K. Singh, S. Sriboonchitta, Construction of cyclic DNA codes over the ring Z4[u]=(u2 -1) based in deletion distance, Theoretical Computer Science 773 (2018) 27–42.
  • [11] B. Feng, S. S. Bai, B. Y. Chen, X. N. Zhou, The constructions of DNA codes from linear self-dual codes over Z4, International Conference on Computer Information Systems and Industrial Applications (CISIA 2015) (2015) 496–498.
  • [12] K. Guenda, T. A. Gulliver, P. Solé, On cyclic DNA codes, IEEE Inter. Sym. Inform. Theory (2013) 121–125.
  • [13] A. R. Hammons, V. Kumar, A. R. Calderbank, N. J. A. Sloane, P. Solé, The Z4-linearity of Kerdock, Preparata, Goethals, and related codes, IEEE Transactions on Information Theory 40(2) (1994) 301–319.
  • [14] J. Liang, L. Wang, On cyclic DNA codes over F2 + uF2, Journal of Applied Mathematics and Computing 51 (2015) 81–91.
  • [15] M. Özen, N. T. Özzaim, N. Aydin, Cyclic codes over Z4+uZ4+u2Z4, Turkish Journal of Mathematics 41 (2017) 1235–1247.
  • [16] A. S. L. Rocha, L. C. B. Faria, J. H. Kleinschmidt, R. Palazzo, M. C. Silva-Filho, DNA sequences generated by Z4-linear codes, IEEE International Symposium on Information Theory (2010) 1320–1324.
  • [17] I. Siap, T. Abualrub, N. Aydin, P. Seneviratne, Skew cyclic codes of arbitrary length, Int. J. Inform. Coding Theory 2 (2011) 10–20.
  • [18] B. Yildiz, I. Siap, Cyclic codes over F2[u]/ (u4-1) and applications to DNA codes, Computers & Mathematics with Applications 63 (2012) 1169–1176.
  • [19] 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: 3, 219 - 231, 15.09.2021
https://doi.org/10.13069/jacodesmath.1000959

Öz

Kaynakça

  • [1] T. Abualrub, R. Oehmke, On the generators of Z4 cyclic codes of length 2e, IEEE Transactions on Information Theory 49 (2003) 2126–2133.
  • [2] T. Abualrub, I. Siap, Cyclic codes over the rings Z2 + uZ2 and Z2 + uZ2 + u2Z2, Des Codes Crypt 42 (2007) 273–287.
  • [3] T. Abualrub, I. Siap, Reversible cyclic codes over Z4, Australasian Journal of Combinatorics 38 (2007) 195–205.
  • [4] L. M. Adleman, Molecular computation of solutions to combinatorial problems, Science 266 (1994) 1021–1024.
  • [5] N. Bennenni, K. Guenda, S. Mesnager, New DNA cyclic codes over rings, Adv. Math. Comp. 11(1) (2017) 83–98.
  • [6] A. Bonnecaze, P. Udaya, Cyclic codes and self-dual codes over F2 + uF2, IEEE Transactions on Information Theory 45 (1999) 1250–1255.
  • [7] D. Boucher, W. Geiselmann, F. Ulmer, Skew cyclic codes, Applied Algebra in Engineering, Communication and Computing 18 (2007) 379–389.
  • [8] D. Boucher, F. Ulmer, Coding with skew polynomial rings, Journal of Symbolic Computation 44 (2009) 1644–1656.
  • [9] Y. Cengellenmis, N. Aydin, A. Dertli, Reversible DNA codes from skew cyclic codes over a ring of order 256, J. Algebra Comb. Discrete Appl. 8(1) (2021) 1–8.
  • [10] H. Q. Dinh, S. Pattanayak, A. K. Singh, S. Sriboonchitta, Construction of cyclic DNA codes over the ring Z4[u]=(u2 -1) based in deletion distance, Theoretical Computer Science 773 (2018) 27–42.
  • [11] B. Feng, S. S. Bai, B. Y. Chen, X. N. Zhou, The constructions of DNA codes from linear self-dual codes over Z4, International Conference on Computer Information Systems and Industrial Applications (CISIA 2015) (2015) 496–498.
  • [12] K. Guenda, T. A. Gulliver, P. Solé, On cyclic DNA codes, IEEE Inter. Sym. Inform. Theory (2013) 121–125.
  • [13] A. R. Hammons, V. Kumar, A. R. Calderbank, N. J. A. Sloane, P. Solé, The Z4-linearity of Kerdock, Preparata, Goethals, and related codes, IEEE Transactions on Information Theory 40(2) (1994) 301–319.
  • [14] J. Liang, L. Wang, On cyclic DNA codes over F2 + uF2, Journal of Applied Mathematics and Computing 51 (2015) 81–91.
  • [15] M. Özen, N. T. Özzaim, N. Aydin, Cyclic codes over Z4+uZ4+u2Z4, Turkish Journal of Mathematics 41 (2017) 1235–1247.
  • [16] A. S. L. Rocha, L. C. B. Faria, J. H. Kleinschmidt, R. Palazzo, M. C. Silva-Filho, DNA sequences generated by Z4-linear codes, IEEE International Symposium on Information Theory (2010) 1320–1324.
  • [17] I. Siap, T. Abualrub, N. Aydin, P. Seneviratne, Skew cyclic codes of arbitrary length, Int. J. Inform. Coding Theory 2 (2011) 10–20.
  • [18] B. Yildiz, I. Siap, Cyclic codes over F2[u]/ (u4-1) and applications to DNA codes, Computers & Mathematics with Applications 63 (2012) 1169–1176.
  • [19] S. Zhu, X. Chen, Cyclic DNA codes over F2 + uF2 + vF2 + uvF2 and their applications, J. Appl. Math. Comput. 55 (2017) 479–493.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Karthick Gowthaman Bu kişi benim

Somi Gupta Bu kişi benim 0000-0003-0104-2993

Cruz Mohan Bu kişi benim

Kenza Guenda Bu kişi benim

Durairajan Chinnapillai Bu kişi benim

Erken Görünüm Tarihi 9 Ekim 2021
Yayımlanma Tarihi 15 Eylül 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 8 Sayı: 3

Kaynak Göster

APA Gowthaman, K., Gupta, S., Mohan, C., Guenda, K., vd. (2021). 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, 8(3), 219-231. https://doi.org/10.13069/jacodesmath.1000959
AMA Gowthaman K, Gupta S, Mohan C, Guenda K, Chinnapillai D. 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. Eylül 2021;8(3):219-231. doi:10.13069/jacodesmath.1000959
Chicago Gowthaman, Karthick, Somi Gupta, Cruz Mohan, Kenza Guenda, ve Durairajan Chinnapillai. “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 8, sy. 3 (Eylül 2021): 219-31. https://doi.org/10.13069/jacodesmath.1000959.
EndNote Gowthaman K, Gupta S, Mohan C, Guenda K, Chinnapillai D (01 Eylül 2021) 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 8 3 219–231.
IEEE K. Gowthaman, S. Gupta, C. Mohan, K. Guenda, ve D. Chinnapillai, “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, c. 8, sy. 3, ss. 219–231, 2021, doi: 10.13069/jacodesmath.1000959.
ISNAD Gowthaman, Karthick vd. “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 8/3 (Eylül 2021), 219-231. https://doi.org/10.13069/jacodesmath.1000959.
JAMA Gowthaman K, Gupta S, Mohan C, Guenda K, Chinnapillai D. 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. 2021;8:219–231.
MLA Gowthaman, Karthick vd. “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, c. 8, sy. 3, 2021, ss. 219-31, doi:10.13069/jacodesmath.1000959.
Vancouver Gowthaman K, Gupta S, Mohan C, Guenda K, Chinnapillai D. 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. 2021;8(3):219-31.