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

On DNA Codes Over the Non-Chain Ring Z4+uZ4+u2Z4\mathbb{Z}_4+u\mathbb{Z}_4+u^2\mathbb{Z}_4 with u3=1u^3=1

In this paper, we present a novel design strategy of DNA codes with length $3n$ over the non-chain ring $R=\mathbb{Z}_4+u\mathbb{Z}_4+u^2\mathbb{Z}_4$ with $64$ elements and $u^3=1$, where $n$ denotes the length of a code over $R$. We first study and analyze a distance conserving map defined over the ring $R$ into the length-$3$ DNA sequences. Then, we derive some conditions on the generator matrix of a linear code over $R$, which leads to a DNA code with reversible, reversible-complement, homopolymer $2$-run-length, and $\frac{w}{3n}$-GC-content constraints for integer $w$ ($0\leq w\leq 3n$). Finally, we propose a new construction of DNA codes using Reed-Muller type generator matrices. This allows us to obtain DNA codes with reversible, reversible-complement, homopolymer $2$-run-length, and $\frac{2}{3}$-GC-content constraints.Comment: This paper has been presented in IEEE Information Theory Workshop (ITW) 2022, Mumbai, INDI

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

Thermodynamically Stable DNA Code Design using a Similarity Significance Model

DNA code design aims to generate a set of DNA sequences (codewords) with minimum likelihood of undesired hybridizations among sequences and their reverse-complement (RC) pairs (cross-hybridization). Inspired by the distinct hybridization affinities (or stabilities) of perfect double helix constructed by individual single-stranded DNA (ssDNA) and its RC pair, we propose a novel similarity significance (SS) model to measure the similarity between DNA sequences. Particularly, instead of directly measuring the similarity of two sequences by any metric/approach, the proposed SS works in a way to evaluate how more likely will the undesirable hybridizations occur over the desirable hybridizations in the presence of the two measured sequences and their RC pairs. With this SS model, we construct thermodynamically stable DNA codes subject to several combinatorial constraints using a sorting-based algorithm. The proposed scheme results in DNA codes with larger code sizes and wider free energy gaps (hence better cross-hybridization performance) compared to the existing methods.Comment: To appear in ISIT 202

DNA Linear Block Codes: Generation, Error-detection and Error-correction of DNA Codeword

In modern age, the increasing complexity of computation and communication technology is leading us towards the necessity of new paradigm. As a result, unconventional approach like DNA coding theory is gaining considerable attention. The storage capacity, information processing and transmission properties of DNA molecules stimulate the notion of DNA coding theory as well as DNA cryptography. In this paper we generate DNA codeword using DNA (n, k) linear block codes which ensures the secure transmission of information. In the proposed code design strategy DNA-based XOR operation (DNAX) is applied for effective construction of DNA codewords which are quadruples generated over the set of alphabets {A,T,G,C}. By worked out examples we explain the use of generator matrix and parity check matrix in encryption and decryption of coded data in the form of short single stranded DNA sequences. The newly developed technique is capable of detecting as well as correcting error in transmission of DNA codewords from sender to the intended receiver.Comment: 23 pages, 1 figure, 5 table