Abstract
In this study we focus on codes over a special family of commutative rings where we are able to construct a map that gives a correspondence between k-bases (k-letter words) of DNA with elements of the ring. By making use of so called coterm polynomials, we are able to solve the reversibility and complement problems in DNA codes and construct DNA codes over this ring.
This study is supported by The Scientific and Technological Research Council of Turkey (TÜBİTAK) (No: 113F071).
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References
Abulraub, T., Ghrayeb, A., Zeng, X.N.: Construction of cyclic codes over GF(4) for DNA computing. Journal of the Franklin Institute 343(4-5), 448–457 (2006)
Adleman, L.: Molecular computation of solutions to combinatorial problems. Science 266, 1021–1024 (1994)
Adleman, L., Rothemund, P.W.K., Roweis, S., Winfree, E.: On applying molecular computation to the Data Encryption Standard. Journal of Computational Biology 6, 53–63 (1999)
Boneh, D., Dunworth, C., Lipton, R.: Breaking DES using molecular computer, Princeton CS Tech-Report, Number CS-TR-489-95 (1995)
Mansuripur, M., Khulbe, P.K., Kuebler, S.M., Perry, J.W., Giridhar, M.S., Peyghambarian, N.: Information Storage and retrieval using macromolecules as storage media, University of Arizona Technical Report (2003)
Oztas, E.S., Siap, I.: Lifted Polynomials Over F 16 and Their Applications to DNA Codes. Filomat 27(3), 459–466 (2013)
Siap, I., Abulraub, T., Ghayreb, A.: Similarity Cyclic DNA Codes over Rings. International Conference on Bioinformatics and Biomedical Engineering, Shanghai, PRC, May 16–18 (2008)
Siap, I., Abulraub, T., Ghrayeb, A.: Cyclic DNA codes over the ring \(\mathbb{F}_2[u]/(u^2-1)\) based on the deletion distance. Journal of the Franklin Institute 346(8), 731–740 (2009)
Yildiz, B., Siap, I.: Cyclic Codes over \(\mathbb{F}_2[u]/(u^4-1)\) and applications to DNA codes. Computers and Mathematics with Applications 63(7), 1169–1176 (2012)
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Oztas, E.S., Siap, I., Yildiz, B. (2014). Reversible Codes and Applications to DNA. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_22
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DOI: https://doi.org/10.1007/978-3-662-44199-2_22
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