# DNA digital data storage and retrieval using algebraic codes

## TL;DR

This paper proposes a novel DNA data storage method using algebraic codes, specifically kernel codes and the Varshamov-Tenengolts algorithm, to address indel errors and stability issues in DNA storage.

## Contribution

It introduces a new coding scheme that combines algebraic codes with error correction tailored for DNA storage, including handling reverse complement constraints.

## Key findings

- Successfully corrects single indel errors in DNA data storage
- Constructs codes of arbitrary length with calculated reverse complement distance
- Addresses DNA stability and secondary structure formation issues

## Abstract

DNA is a promising storage medium, but its stability and occurrence of Indel errors pose a significant challenge. The relative occurrence of Guanine(G) and Cytosine(C) in DNA is crucial for its longevity, and reverse complementary base pairs should be avoided to prevent the formation of a secondary structure in DNA strands. We overcome these challenges by selecting appropriate group homomorphisms. For storing and retrieving information in DNA strings we use kernel code and the Varshamov-Tenengolts algorithm. The Varshamov-Tenengolts algorithm corrects single indel errors. Additionally, we construct codes of any desired length (n) while calculating its reverse complement distance based on the value of n.