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- Arkadii G. D'yachkov, Péter L. Erdös, +5 authors P. Scott White
- J. Comb. Optim.
- 2003

We describe how deletion-correcting codes may be enhanced to yield codes with double-strand DNA-sequence codewords. This enhancement involves abstractions of the pertinent aspects of DNA; it nevertheless ensures specificity of binding for all pairs of single strands derived from its codewords—the key desideratum of DNA codes– i.e. with binding feasible only… (More)

{ We consider a class of superimposed codes 1, 2] for the search model of A. Renyi 3]. A lower bound on the code length is obtained and optimal superimposed codes are presented.

- A G D 'yachkov, V V Rykov
- 2013

A new lower bound for the length of disjunctive codes [I] is proved. An upper bound obtained by the method of random coding is given. columns (of 0 and 1) of length N. The componentwise Boolean sum u=u(1)Vu(2)V ... Vu(s) of columns u(l), u(2), ... , u(s) is what we call binary column u = (ul' u 2 , • • • , uN} whose components are defined by the expressions… (More)

- Arkadii G. D'yachkov, Anthony J. Macula, Vyacheslav V. Rykov
- IEEE Trans. Information Theory
- 2000

- Anthony J. Macula, Vyacheslav V. Rykov, Sergey Yekhanin
- Discrete Applied Mathematics
- 2004

Let [t] represent a nite population with t elements. Suppose we have an unknown d-family of k-subsets of [t]. We refer to as the set of positive k-complexes.I nt h egroup testing for complexes problem, must be identied by performing 0, 1 tests on subsets or pools of [t]. A pool is said to be positive if it completely contains a complex; otherwise the pool… (More)

- Arkadii G. D'yachkov, Anthony J. Macula, Wendy K. Pogozelski, Thomas E. Renz, Vyacheslav V. Rykov, David C. Torney
- Journal of Computational Biology
- 2006

We discuss the concept of t-gap block isomorphic subsequences and use it to describe new abstract string metrics that are similar to the Levenshtein insertion-deletion metric. Some of the metrics that we define can be used to model a thermodynamic distance function on single-stranded DNA sequences. Our model captures a key aspect of the nearest neighbor… (More)

- Morgan A. Bishop, Arkadii G. D'yachkov, Anthony J. Macula, Thomas E. Renz, Vyacheslav V. Rykov
- Journal of Computational Biology
- 2007

DNA nanotechnology often requires collections of oligonucleotides called "DNA free energy gap codes" that do not produce erroneous crosshybridizations in a competitive muliplexing environment. This paper addresses the question of how to design these codes to accomplish a desired amount of work within an acceptable error rate. Using a statistical… (More)

- Leonid A. Bassalygo, Vyacheslav V. Rykov
- Probl. Inf. Transm.
- 2013