Tersinirlik Problemi Hakkında

Öz

Bu çalışmada, u^2=u, v^2=v, uv=vu ve Z_4={0,1,2,3} olmak üzere R=Z_4+uZ_4+vZ,_4+uvZ_4 sonlu halkası üzerinde tanımlı çarpık devirli kodlar kullanılarak, tersinirlik probleminin özel bir hali çözülmüş ve tersinir DNA kodlar elde edilmiştir.

Anahtar Kelimeler

• Çarpık devirli kodlar,Tersinirlik problemi

On the Reversibility Problem for DNA 4-bases

Öz

By defining a non-trivial automorphism over R=Z_4+uZ_4+vZ,_4+uvZ_4 where u^2=u, v^2=v, uv=vu and Z_4={0,1,2,3}, the skew cyclic codes over the finite ring R are introduced. By using the skew cyclic codes over R, it is solved the reversibility problem for DNA 4-bases. Thanks to this, the reversible DNA codes are obtained.

Anahtar Kelimeler

• Skew cyclic codes,Reversibility problem

Kaynakça

1. Adleman L. 1994. “Molecular computation of the solutions to combinatorial problems”, Science, 266,1021-1024.
2. Bayram A., Oztas E., Siap I. 2015. “Codes over and some DNA applications”, Designs, Codes and Cryptography, DOI: 10.107/s10623-015-01008.
3. Cengellenmis Y., Dertli A. 2019. “On the skew cyclic codes and the reversibility problem for DNA 4-bases”, Mathematics in Computer Science, to be accepted.
4. Dertli A., Cengellenmis Y. 2017. “On cyclic DNA codes over the rings and ”, Biomath, 6, 1712167.
5. Gursoy F., Oztas S. E., Siap I. 2017. “Reversible DNA codes over ”, American Institude of Mathematical Sciences, 11, 307-312.
6. Gursoy F., Oztas S. E.,Ozkan A. 2017. “Reversible DNA codes over a family of non-chain ring”, arXiv:1711.02385v1.
7. Head, T. 1987. “Formal language theory and DNA: an analysis of the generative capacity of specific recombinant behaviors”, Bulletin of mathematical biology, 49, 737-759.
8. Kumar, N., Singh A. K. 2018. “DNA computing over the ring ”, International Journal of Biomathematics , 11, 1850090.