Efficient and Explicit Balanced Primer Codes

TL;DR

This paper presents explicit constructions of error-correcting primer codes for DNA data storage, combining cyclic codes, BCH codes, and balancing techniques to enable efficient, balanced, and error-resistant DNA primer design.

Contribution

It introduces novel explicit constructions of balanced error-correcting codes for DNA primers using cyclic and BCH codes with efficient encoding algorithms.

Findings

Infinite families of primer sets with error correction and balancing properties.

Efficient encoding algorithms for the constructed codes.

Application to DNA computing and data storage.

Abstract

To equip DNA-based data storage with random-access capabilities, Yazdi et al. (2018) prepended DNA strands with specially chosen address sequences called primers and provided certain design criteria for these primers. We provide explicit constructions of error-correcting codes that are suitable as primer addresses and equip these constructions with efficient encoding algorithms. Specifically, our constructions take cyclic or linear codes as inputs and produce sets of primers with similar error-correcting capabilities. Using certain classes of BCH codes, we obtain infinite families of primer sets of length $n$, minimum distance $d$ with $(d + 1) \log_4 n + O(1)$ redundant symbols. Our techniques involve reversible cyclic codes (1964), an encoding method of Tavares et al. (1971) and Knuth's balancing technique (1986). In our investigation, we also construct efficient and explicit binary balanced error-correcting codes and codes for DNA computing.