# On the Design of Codes for DNA Computing: Secondary Structure Avoidance Codes

## TL;DR

This paper presents explicit constructions of DNA codes that completely avoid secondary structures of any stem length, improving code rates and providing efficient encoding methods for DNA computing applications.

## Contribution

The work introduces novel explicit constructions for DNA codes that eliminate secondary structures of arbitrary stem length, surpassing previous code rate limits.

## Key findings

- Constructed DNA codes with rate 1.3031 bits/nt for m=3.
- Achieved efficient encoding with only one redundant symbol for large m.
- Provided methods to avoid secondary structures of any stem length ≥ m.

## Abstract

In this work, we investigate a challenging problem, which has been considered to be an important criterion in designing codewords for DNA computing purposes, namely secondary structure avoidance in single-stranded DNA molecules. In short, secondary structure refers to the tendency of a single-stranded DNA sequence to fold back upon itself, thus becoming inactive in the computation process. While some design criteria that reduces the possibility of secondary structure formation has been proposed by Milenkovic and Kashyap (2006), the main contribution of this work is to provide an explicit construction of DNA codes that completely avoid secondary structure of arbitrary stem length. Formally, given codeword length n and arbitrary integer m>=2, we provide efficient methods to construct DNA codes of length n that avoid secondary structure of any stem length more than or equal to m. Particularly, when m = 3, our constructions yield a family of DNA codes of rate 1.3031 bits/nt, while the highest rate found in the prior art was 1.1609 bits/nt. In addition, for m>=3log n + 4, we provide an efficient encoder that incurs only one redundant symbol.