Linear and nonlinear constructions of DNA codes with Hamming distance d, constant GC-content and a reverse-complement constraint

AbstractIn a previous paper, the authors used cyclic and extended cyclic constructions to obtain codes over an alphabet {A,C,G,T} satisfying a Hamming distance constraint and a GC-content constraint. These codes are applicable to the design of synthetic DNA strands used in DNA microarrays, as DNA tags in chemical libraries and in DNA computing. The GC-content constraint specifies that a fixed number of positions are G or C in each codeword, which ensures uniform melting temperatures. The Hamming distance constraint is a step towards avoiding unwanted hybridizations. This approach extended the pioneering work of Gaborit and King. In the current paper, another constraint known as a reverse-complement constraint is added to further prevent unwanted hybridizations.Many new best codes are obtained, and are reproducible from the information presented here. The reverse-complement constraint is handled by searching for an involution with 0 or 1 fixed points, as first done by Gaborit and King. Linear codes and additive codes over GF(4) and their cosets are considered, as well as shortenings of these codes. In the additive case, codes obtained from two different mappings from GF(4) to {A,C,G,T} are considered

On Conflict Free DNA Codes

DNA storage has emerged as an important area of research. The reliability of DNA storage system depends on designing the DNA strings (called DNA codes) that are sufficiently dissimilar. In this work, we introduce DNA codes that satisfy a special constraint. Each codeword of the DNA code has a specific property that any two consecutive sub-strings of the DNA codeword will not be the same (a generalization of homo-polymers constraint). This is in addition to the usual constraints such as Hamming, reverse, reverse-complement and $GC$-content. We believe that the new constraint will help further in reducing the errors during reading and writing data into the synthetic DNA strings. We also present a construction (based on a variant of stochastic local search algorithm) to calculate the size of the DNA codes with all the above constraints, which improves the lower bounds from the existing literature, for some specific cases. Moreover, a recursive isometric map between binary vectors and DNA strings is proposed. Using the map and the well known binary codes we obtain few classes of DNA codes with all the constraints including the property that the constructed DNA codewords are free from the hairpin-like secondary structures.Comment: 12 pages, Draft (Table VI and Table VII are updated

On DNA codes from a family of chain rings

In this work, we focus on reversible cyclic codes which correspond to reversible DNA codes or reversible-complement DNA codes over a family of finite chain rings, in an effort to extend what was done by Yildiz and Siap in [20]. The ring family that we have considered are of size $2^{2^k}$, $k=1,2, \cdots$ and we match each ring element with a DNA $2^{k-1}$-mer. We use the so-called $u^2$-adic digit system to solve the reversibility problem and we characterize cyclic codes that correspond to reversible-complement DNA-codes. We then conclude our study with some examples

Linear Size Optimal q-ary Constant-Weight Codes and Constant-Composition Codes

An optimal constant-composition or constant-weight code of weight $w$ has linear size if and only if its distance $d$ is at least $2w-1$. When $d\geq 2w$, the determination of the exact size of such a constant-composition or constant-weight code is trivial, but the case of $d=2w-1$ 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 $w$ and distance $2w-1$ 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 $w$ and distance $2w-1$ 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 $w$ and distance $2w-1$ are also determined for all $w\leq 6$, except in two cases.Comment: 12 page

Compressive Sensing DNA Microarrays

Compressive sensing microarrays (CSMs) are DNA-based sensors that operate using group testing and compressive sensing (CS) principles. In contrast to conventional DNA microarrays, in which each genetic sensor is designed to respond to a single target, in a CSM, each sensor responds to a set of targets. We study the problem of designing CSMs that simultaneously account for both the constraints from CS theory and the biochemistry of probe-target DNA hybridization. An appropriate cross-hybridization model is proposed for CSMs, and several methods are developed for probe design and CS signal recovery based on the new model. Lab experiments suggest that in order to achieve accurate hybridization profiling, consensus probe sequences are required to have sequence homology of at least 80% with all targets to be detected. Furthermore, out-of-equilibrium datasets are usually as accurate as those obtained from equilibrium conditions. Consequently, one can use CSMs in applications in which only short hybridization times are allowed

Reversible codes and applications to DNA codes over F42t[u]/(u2−1) F_{4^{2t}}[u]/(u^2-1)

Let $n \geq 1$ be a fixed integer. Within this study, we present a novel approach for discovering reversible codes over rings, leveraging the concept of $r$-glifted polynomials. This technique allows us to achieve optimal reversible codes. As we extend our methodology to the domain of DNA codes, we establish a correspondence between $4t$-bases of DNA and elements within the ring $R_{2t} = F_{4^{2t}}[u]/(u^{2}-1)$. By employing a variant of $r$-glifted polynomials, we successfully address the challenges of reversibility and complementarity in DNA codes over this specific ring. Moreover, we are able to generate reversible and reversible-complement DNA codes that transcend the limitations of being linear cyclic codes generated by a factor of $x^n-1$