Advertisement

A Special Class of Additive Cyclic Codes for DNA Computing

  • Taher Abualrub
  • Ali Ghrayeb
  • Xiang Nian Zeng
Conference paper

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.

Keywords

Cyclic Code Additive Code Reversible Complement Weight Enumerator Hamiltonian Path Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    L. Adleman (1994), “Molecular Computation of Solutions to Combinatorial Problems,” Science, v. 266, 1021–1024.Google Scholar
  2. [2]
    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.Google Scholar
  3. [3]
    P. Gaborit and O. King, “Linear constructions for DNA codes,” Preprint.Google Scholar
  4. [4]
    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.Google Scholar
  5. [5]
    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.Google Scholar
  6. [6]
    L. Kari, R. Kitto, G. Thierrin (2003), “Codes, involutions, and DNA encoding,” Lecture Notes in Computer Science 2300, Springer Verlag, 376–393.Google Scholar
  7. [7]
    O. King (2003), “Bounds for DNA codes with constant GC-content,” The Electronic Journal of Combinatorics, vol. 10, 1–13.Google Scholar
  8. [8]
    A. Marathe, A. E. Condon and R. M. Corn (2001), “On Combinatorial DNA word design,” Journal of Computational Biology, vol.8, 201–220.CrossRefGoogle Scholar
  9. [9]
    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.CrossRefGoogle Scholar
  10. [10]
    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.Google Scholar
  11. [11]
    F. J. MacWilliams and N. J. A. Sloane (1997), The Theory of Error-Correcting Codes, Ninth Impression, North-Holland, Amsterdam.Google Scholar
  12. [12]
    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.MathSciNetCrossRefGoogle Scholar
  13. [13]
    J. L. Massey (1964), “Reversible Codes,” Information and Control vol. 7, pp. 369–380.MATHMathSciNetCrossRefGoogle Scholar
  14. [14]
    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.MathSciNetCrossRefGoogle Scholar
  15. [15]
    T. Abualrub and A. Ghrayeb (submitted 2004), “On the construction of Cyclic Codes for DNA Computing,”.Google Scholar
  16. [16]
    D. C. Tublan, “Tables of DNA codes,” http://www.cs.ubs.ca/~dctulpan/papers/dna8/tables/index.html.Google Scholar

Copyright information

© Springer-Verlag/Wien 2005

Authors and Affiliations

  • Taher Abualrub
    • 1
  • Ali Ghrayeb
    • 2
  • Xiang Nian Zeng
    • 2
  1. 1.Department of MathematicsAmerican University of SharjahUAE
  2. 2.Department of Electrical and Computer EngineeringConcordia UniversityMontrealCanada

Personalised recommendations