On a class of codes for the insertion-deletion metric

D’yachkov, Arkadii G.; Torney, David C.; Vilenkin, Pavel A.; White, S.

doi:10.1109/isit.2002.1023644

Cited by 5 publications

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“…Definition 3 [1,3]. Let a complement operation be defined on the alphabet A that takes each element a ∈ A to a complement elementā ∈ A.…”

Section: Notations Definitions and Resultsmentioning

confidence: 99%

“…Definition 4 [1,3]. A code X is called an (n, D) DNA code based on a similarity function S = S(x, y) (briefly, (n, D)-code) if the following two conditions hold:…”

Section: Notations Definitions and Resultsmentioning

confidence: 99%

“…Theorem 1 presents our announced results [3] about lower bounds for DNA codes based on the deletion similarity. Let d = d λ q be a the unique root of the equation…”

Section: Notations Definitions and Resultsmentioning

confidence: 99%

“…More exactly, one needs to construct a set of DNA sequences (a DNA code [1,3]) containing any sequence X together with its reverse-complement X such that formation of a WC duplex from these sequences should energetically be more favorable than formation of a non-WC duplexes. For this, there should exist a temperature threshold much below the melting points of all WC duplexes and much above…”

Section: Introduction and Biological Motivationmentioning

confidence: 99%

“…For instance, we cannot apply the best known random coding bound [11] on the rate of deletion-correcting codes because these bounds were proved for codes which are not invariant under the reverse-complement transformation. For the deletion similarity, the best known random coding bounds on the rate of DNA codes were established in our papers [1,3]. The second traditional coding theory problem for DNA codes is to present constructions of DNA codes.…”

Section: Introduction and Biological Motivationmentioning

confidence: 99%

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On DNA Codes

et al. 2005

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We develop and study the concept of similarity functions for q-ary sequences. For the case q = 4, these functions can be used for a mathematical model of the DNA duplex energy [1,2], which has a number of applications in molecular biology. Based on these similarity functions, we define a concept of DNA codes [1]. We give brief proofs for some of our unpublished results [3] connected with the well-known deletion similarity function [4][5][6]. This function is the length of the longest common subsequence; it is used in the theory of codes that correct insertions and deletions [5]. Principal results of the present paper concern another function, called the similarity of blocks. The difference between this function and the deletion similarity is that the common subsequences under consideration should satisfy an additional biologically motivated [2] block condition, so that not all common subsequences are admissible. We prove some lower bounds on the size of an optimal DNA code for the block similarity function. We also consider a construction of close-to-optimal DNA codes which are subcodes of the parity-check one-error-detecting code in the Hamming metric [7]. 0032-9460/05/4104-0349 c 2005 Pleiades Publishing, Inc.

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“…Definition 3 [1,3]. Let a complement operation be defined on the alphabet A that takes each element a ∈ A to a complement elementā ∈ A.…”

Section: Notations Definitions and Resultsmentioning

confidence: 99%

“…Definition 4 [1,3]. A code X is called an (n, D) DNA code based on a similarity function S = S(x, y) (briefly, (n, D)-code) if the following two conditions hold:…”

Section: Notations Definitions and Resultsmentioning

confidence: 99%

“…Theorem 1 presents our announced results [3] about lower bounds for DNA codes based on the deletion similarity. Let d = d λ q be a the unique root of the equation…”

Section: Notations Definitions and Resultsmentioning

confidence: 99%

Section: Introduction and Biological Motivationmentioning

confidence: 99%

Section: Introduction and Biological Motivationmentioning

confidence: 99%

See 3 more Smart Citations