A new preprint on the Geometry of Codes for Random Access in DNA Storage is now available on arXiv here.
It was written by algebra group members Anina Gruica and Maria Montanucci together with Ferdinando Zullo from the University of Campania, Italy. The work was initiated when Ferdinando visited the algebra group in connection with Maria’s Villum YIP project CREATE.
Effective and reliable data retrieval is critical for the feasibility of DNA storage, and the development of random access efficiency plays a key role in its practicality and reliability. In this paper, we study the Random Access Problem, which asks to compute the expected number of samples one needs in order to recover an information strand. Unlike previous work, we took a geometric approach to the problem, aiming to understand which geometric structures lead to codes that perform well in terms of reducing the random access expectation (Balanced Quasi-Arcs). As a consequence, two main results are obtained. The first is a construction for k=3 that outperforms previous constructions aiming to reduce the random access expectation. The second is the proof of a conjecture for rate 1/2 codes in any dimension.