25 research outputs found
Bounds for DNA codes with constant GC-content
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.Comment: 13 pages, no figures; a few references added and typos correcte
Improved Lower Bounds for Constant GC-Content DNA Codes
The design of large libraries of oligonucleotides having constant GC-content
and satisfying Hamming distance constraints between oligonucleotides and their
Watson-Crick complements is important in reducing hybridization errors in DNA
computing, DNA microarray technologies, and molecular bar coding. Various
techniques have been studied for the construction of such oligonucleotide
libraries, ranging from algorithmic constructions via stochastic local search
to theoretical constructions via coding theory. We introduce a new stochastic
local search method which yields improvements up to more than one third of the
benchmark lower bounds of Gaborit and King (2005) for n-mer oligonucleotide
libraries when n <= 14. We also found several optimal libraries by computing
maximum cliques on certain graphs.Comment: 4 page
Group Divisible Codes and Their Application in the Construction of Optimal Constant-Composition Codes of Weight Three
The concept of group divisible codes, a generalization of group divisible
designs with constant block size, is introduced in this paper. This new class
of codes is shown to be useful in recursive constructions for constant-weight
and constant-composition codes. Large classes of group divisible codes are
constructed which enabled the determination of the sizes of optimal
constant-composition codes of weight three (and specified distance), leaving
only four cases undetermined. Previously, the sizes of constant-composition
codes of weight three were known only for those of sufficiently large length.Comment: 13 pages, 1 figure, 4 table
The PBD-Closure of Constant-Composition Codes
We show an interesting PBD-closure result for the set of lengths of
constant-composition codes whose distance and size meet certain conditions. A
consequence of this PBD-closure result is that the size of optimal
constant-composition codes can be determined for infinite families of parameter
sets from just a single example of an optimal code. As an application, the size
of several infinite families of optimal constant-composition codes are derived.
In particular, the problem of determining the size of optimal
constant-composition codes having distance four and weight three is solved for
all lengths sufficiently large. This problem was previously unresolved for odd
lengths, except for lengths seven and eleven.Comment: 8 page
Linear Size Optimal q-ary Constant-Weight Codes and Constant-Composition Codes
An optimal constant-composition or constant-weight code of weight has
linear size if and only if its distance is at least . When , the determination of the exact size of such a constant-composition or
constant-weight code is trivial, but the case of has been solved
previously only for binary and ternary constant-composition and constant-weight
codes, and for some sporadic instances.
This paper provides a construction for quasicyclic optimal
constant-composition and constant-weight codes of weight and distance
based on a new generalization of difference triangle sets. As a result,
the sizes of optimal constant-composition codes and optimal constant-weight
codes of weight and distance are determined for all such codes of
sufficiently large lengths. This solves an open problem of Etzion.
The sizes of optimal constant-composition codes of weight and distance
are also determined for all , except in two cases.Comment: 12 page