# On Conflict Free DNA Codes

## TL;DR

This paper introduces a new class of DNA codes with a unique consecutive substring constraint, enhancing error reduction in DNA data storage, and provides constructions that improve existing bounds using stochastic local search and binary code mappings.

## Contribution

It proposes a novel consecutive substring constraint for DNA codes, develops a construction method that improves lower bounds, and introduces a binary-to-DNA mapping to generate codes free from secondary structures.

## Key findings

- New DNA codes with the consecutive substring constraint are constructed.
- The construction improves lower bounds on code size compared to previous work.
- Some codes are guaranteed to be free from hairpin-like secondary structures.

## Abstract

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.