Cyclic DNA codes over the ring $\mathbb{Z}_4+u\mathbb{Z}_4+u^2\mathbb{Z}_4$
Cyclic DNA codes over the ring $\mathbb{Z}_4+u\mathbb{Z}_4+u^2\mathbb{Z}_4$
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.
Keywords:
DNA codes Skew codes, Reversible codes, DNA codes, Skew codes, Reversible codes,
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- [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.
- Başlangıç: 2015
- Yayıncı: İrfan ŞİAP
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