scholarly journals Improved Lower Bounds for Constant GC-Content DNA Codes

2008 ◽  
Vol 54 (1) ◽  
pp. 391-394 ◽  
Author(s):  
Yeow Meng Chee ◽  
San Ling
Keyword(s):  
Lower Bounds ◽  
Gc Content ◽  
Dna Codes

scholarly journals Bounds for DNA Codes with Constant GC-Content

10.37236/1726 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Oliver D. King
Keyword(s):  
Lower Bounds ◽  
Hamming Distance ◽  
Gc Content ◽  
Maximum Size ◽  
Additional Constraint ◽  
Upper And Lower Bounds ◽  
Dna Codes ◽  
Minimum Hamming Distance ◽  
Reverse Complement

We derive theoretical upper and lower bounds on the maximum size of DNA codes of length $n$ with constant GC-content $w$ and minimum Hamming distance $d$, both with and without the additional constraint that the minimum Hamming distance between any codeword and the reverse-complement of any codeword be at least $d$. We also explicitly construct codes that are larger than the best previously-published codes for many choices of the parameters $n$, $d$ and $w$.

Lower Bounds of DNA Codes with Reverse Constraint

2010 ◽  
Vol 7 (10) ◽  
pp. 2072-2076
Author(s):  
Qiang Zhang ◽  
Chunxia Xu
Keyword(s):  
Lower Bounds ◽  
Dna Codes

scholarly journals Construction of Dual Cyclic Codes over {F}_{2}[u,v]/ for DNA Computation

2018 ◽  
Vol 68 (5) ◽  
pp. 467-472
Author(s):  
Manoj Kumar Singh ◽  
Abhay Kumar Singh ◽  
Narendra Kumar ◽  
Pooja Mishra ◽  
Indivar Gupta
Keyword(s):  
Cyclic Codes ◽  
Gc Content ◽  
Inner Product ◽  
Dual Codes ◽  
Dna Computation ◽  
Dna Codes ◽  
Reverse Complement

Here, we assume the construction of cyclic codes over ℜ={F}_{2}[u,v]/ < u^2, v^2 - v, uv - vu >. In particular, dual cyclic codes over ℜ= {F}_{2}[u]/ <u^2> with respect to Euclidean inner product are discussed. The cyclic dual codes over ℜ are studied with respect to DNA codes (reverse and reverse complement). Many interesting results are obtained. Some examples are also provided, which explain the main results. The GC-Content and DNA codes over ℜ are discussed. We summarise the article by giving a special DNA table.

scholarly journals The DNA Word Design Problem: A New Constraint Model and New Results

2017 ◽  
Author(s):  
Michael Codish ◽  
Michael Frank ◽  
Vitaly Lagoon
Keyword(s):  
Lower Bounds ◽  
Design Problem ◽  
Coding Theory ◽  
Hamming Distance ◽  
Fundamental Problem ◽  
Boolean Satisfiability ◽  
Maximum Cardinality ◽  
Dna Codes ◽  
Constraint Model ◽  
Additional Constraints

A fundamental problem in coding theory concerns the computation of the maximum cardinality of a set S of length n code words over an alphabet of size q, such that every pair of code words has Hamming distance at least d, and the set of additional constraints U on S is satisfied. This problem has application in several areas, one of which is the design of DNA codes where q=4 and the alphabet is {A,C,G,T}. We describe a new constraint model for this problem and demonstrate that it improves on previous solutions (computes better lower bounds) for various instances of the problem. Our approach is based on a clustering of DNA words into small sets of words. Solutions are then obtained as the union of such clusters. Our approach is SAT based: we specify constraints on clusters of DNA words and solve these using a Boolean satisfiability solver.

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