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International Workshop on Coding and Cryptography

WCC 2005: Coding and Cryptography pp 100–119Cite as

On the Design of Codes for DNA Computing

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 3969))

Abstract

In this paper, we describe a broad class of problems arising in the context of designing codes for DNA computing. We primarily focus on design considerations pertaining to the phenomena of secondary structure formation in single-stranded DNA molecules and non-selective cross-hybridization. Secondary structure formation refers to the tendency of single-stranded DNA sequences to fold back upon themselves, thus becoming inactive in the computation process, while non-selective cross-hybridization refers to unwanted pairing between DNA sequences involved in the computation process. We use the Nussinov-Jacobson algorithm for secondary structure prediction to identify some design criteria that reduce the possibility of secondary structure formation in a codeword. These design criteria can be formulated in terms of constraints on the number of complementary pair matches between a DNA codeword and some of its shifts. We provide a sampling of simple techniques for enumerating and constructing sets of DNA sequences with properties that inhibit non-selective hybridization and secondary structure formation. Novel constructions of such codes include using cyclic reversible extended Goppa codes, generalized Hadamard matrices, and a binary mapping approach. Cyclic code constructions are particularly useful in light of the fact we prove that the presence of a cyclic structure reduces the complexity of testing DNA codes for secondary structure formation.

This work was supported in part by a research grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada. Portions of this work were presented at the 2005 IEEE International Symposium on Information Theory (ISIT’05) held in Adelaide, Australia.

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Author information

Authors and Affiliations

  1. University of Colorado, Boulder, CO, 80309, USA

    Olgica Milenkovic

  2. Queen’s University, Kingston, ON, K7L 3N6, Canada

    Navin Kashyap

Authors
  1. Olgica Milenkovic
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  2. Navin Kashyap
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Editor information

Editors and Affiliations

  1. Dept. of Informatics, University of Bergen, N-5020, Bergen, Norway

    Øyvind Ytrehus

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© 2006 Springer-Verlag Berlin Heidelberg

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Milenkovic, O., Kashyap, N. (2006). On the Design of Codes for DNA Computing. In: Ytrehus, Ø. (eds) Coding and Cryptography. WCC 2005. Lecture Notes in Computer Science, vol 3969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11779360_9

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  • DOI: https://doi.org/10.1007/11779360_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35481-9

  • Online ISBN: 978-3-540-35482-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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