Abstract
In this paper, we study a special class of nonbinary additive cyclic codes over GF(4) which we call reversible complement cyclic codes. Such codes are suitable for constructing codewords for DNA computing. We develop the theory behind constructing the set of generator polynomials for these codes. We study, as an example, all length—7 codes over GF(4) and list those that have the largest minimum Hamming distance and largest number of codewords.
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References
L. Adleman (1994), “Molecular Computation of Solutions to Combinatorial Problems,” Science, v. 266, 1021–1024.
R. Deaton, R. Murphy, M. Garzon, D. R. Franceschetti, S. E. Stevens (1998), “Good encoding for DNA-based solutions to combinatorial problems,” Proceedings of DNA-Based Computers II, Princeton. In AMS DIMACS Series, vol. 44, L. F. Landweber, E, Baum Eds., 247–258.
P. Gaborit and O. King, “Linear constructions for DNA codes,” Preprint.
M. Garzon, P. Neathery, R. Deaton, M. Garzon, R. C. Murphy, D. R. Franceschetti, S. E. Stevens Jr. (1997), “A new metric for DNA computing” Second Annual Genetic Programming Conference, Stanford, CA, 472–478.
M. Garzon, R. Deaton, L. F. Nino, S. E. Stevens Jr., M. Wittner (1998), “Genome encoding for DNA computing,” Proceedings of the Third Genetic Programming Conference, Madison, WI, 684–690.
L. Kari, R. Kitto, G. Thierrin (2003), “Codes, involutions, and DNA encoding,” Lecture Notes in Computer Science 2300, Springer Verlag, 376–393.
O. King (2003), “Bounds for DNA codes with constant GC-content,” The Electronic Journal of Combinatorics, vol. 10, 1–13.
A. Marathe, A. E. Condon and R. M. Corn (2001), “On Combinatorial DNA word design,” Journal of Computational Biology, vol.8, 201–220.
A. G. Frutos, Q. Liu, A. J. Thiel, A. M. W. Sanner, A. E. Condon, L. M. Smith and R. M. Corn (1997), “Demonstration of a word design strategy for DNA computing on surfaces,” Nucleic Acids Research, vol. 25, 4748–4757.
V. Rykov, A. J. Macula, D. Torney, P. White (2001), “DNA sequences and quaternary cyclic codes,” IEEE ISIT 2001, Washington, DC, June 24–29, pp.248–248.
F. J. MacWilliams and N. J. A. Sloane (1997), The Theory of Error-Correcting Codes, Ninth Impression, North-Holland, Amsterdam.
A. R. Calderbank, E. M. Rains, P. W. Shor, and Neil J. A. Sloane (1998), “Quantum error correction via codes over GF(4),” IEEE Trans. Info. Theory, vol. 44, no. 4, 1369–1387.
J. L. Massey (1964), “Reversible Codes,” Information and Control vol. 7, pp. 369–380.
T. Abualrub and R. Oehmke (2003), “On the generators of Z4 cyclic codes of Length 2e,” IEEE Trans. Info. Theory, vol. 49, no. 9, pp. 2126–2133.
T. Abualrub and A. Ghrayeb (submitted 2004), “On the construction of Cyclic Codes for DNA Computing,”.
D. C. Tublan, “Tables of DNA codes,” http://www.cs.ubs.ca/~dctulpan/papers/dna8/tables/index.html.
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Abualrub, T., Ghrayeb, A., Zeng, X.N. (2005). A Special Class of Additive Cyclic Codes for DNA Computing. In: Ribeiro, B., Albrecht, R.F., Dobnikar, A., Pearson, D.W., Steele, N.C. (eds) Adaptive and Natural Computing Algorithms. Springer, Vienna. https://doi.org/10.1007/3-211-27389-1_68
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DOI: https://doi.org/10.1007/3-211-27389-1_68
Publisher Name: Springer, Vienna
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