Abstract
In this paper, we discuss a general notion of similarity function between two sequences which is based on their common subsequences. This notion arises in some applications of molecular biology [14]. We introduce the concept of similarity codes and study the logarithmic asymptotics for the size of optimal codes. Our mathematical results announced in [13] correspond to the longest common subsequence (LCS) similarity function [2] which leads to a special subclass of these codes called reverse-complement (RC) similarity codes. RC codes for additive similarity functions have been studied in previous papers [9,10,11,12].
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References
Massey, J.L.: Reversible codes. Information and Control 7, 369–380 (1964)
Levenshtein, V.I.: Binary codes capable of correcting deletions, insertions, and reversals. J. Soviet Phys.—Doklady 10, 707–710 (1966)
Levenshtein, V.I.: Elements of coding theory (in Russian). In: Discrete Mathematics and Mathematical Problems of Cybernetics, Moscow, Nauka, pp. 207–305 (1974)
McEliece, R.J., Rodemich, E.R., Rumsey Jr., H., Welch, L.R.: New upper bounds on the rate of a code via the Delsarte—MacWilliams inequalities. IEEE Trans. Inform. Theory 23(2), 157–166 (1977)
MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam, The Netherlands (1977)
Breslauer, K.J., Frank, R., Blöcker, H., Marky, L.A.: Predicting DNA duplex stability from the base sequence. Proc. Nat. Acad. Sci. USA (Biochemistry) 83, 3746–3750 (1986)
Waterman, M.S. (ed.): Mathematical Methods for DNA Sequences. CRC Press, Inc., Boca Raton, Florida (1989)
Dancik, V.: Expected length of longest common subsequences, Ph.D. dissertation, University of Warwick (1994)
D’yachkov, A.G., Torney, D.C.: On similarity codes. IEEE Trans. Inform. Theory 46(4), 1558–1564 (2000)
D’yachkov, A.G., Torney, D.C., Vilenkin, P.A., White, P.S.: Reverse–complement similarity codes for DNA sequences. In: Proc. of ISIT–2000, Sorrento, Italy (July 2000)
Vilenkin, P.A.: Some asymptotic problems of combinatorial coding theory and information theory (in Russian), Ph.D. dissertation, Moscow State University (2000)
Rykov, V.V., Macula, A.J., Korzelius, C.M., Engelhart, D.C., Torney, D.C., White, P.S.: DNA sequences constructed on the basis of quaternary cyclic codes. In: Proc. of 4-th World Multiconference on Systemics, Cybernetics and Informatics, Orlando, Florida, USA (July 2000)
D’yachkov, A.G., Torney, D.C., Vilenkin, P.A., White, P.S.: On a class of codes for the insertion-deletion metric. In: Proc. of ISIT–2002, Lausanne, Switzerland (July 2002)
D’yachkov, A.G., Erdos, P.L., Macula, A.J., Rykov, V.V., Torney, D.C., Tung, C.-S., Vilenkin, P.A., White, P.S.: Exordium for DNA codes. Journal of Combinatorial Optimization 7(4) (2003)
D’yachkov, A.G., Macula, A.J., Pogozelski, W.K., Renz, T.E., Rykov, V.V., Torney, D.C.: A weighted insertion–deletion stacked pair thermodynamic metric for DNA codes. In: The Tenth International Meeting on DNA Computing, Milano-Bicocca, Italy (2004)
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D’yachkov, A., Torney, D., Vilenkin, P., White, S. (2006). Reverse–Complement Similarity Codes. In: Ahlswede, R., et al. General Theory of Information Transfer and Combinatorics. Lecture Notes in Computer Science, vol 4123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889342_52
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DOI: https://doi.org/10.1007/11889342_52
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-46244-6
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