New preprint on the Geometry of Codes for Random Access in DNA Storage

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.

The algebra group is happy to host Researcher Ferdinando Zullo from the University of Campania “Luigi Vanvitelli” as a guest in the period October 9 – October 19. Ferdinando has already collaborated with both Maria and Anina in the past, obtaining interesting results between the interplay of finite geometry/combinatorics and coding theory.

During his stay Ferdinando, as a key partner of Villum YIP project CREATE, will work with Anina and Maria on the use of geometric tools to construct good codes for random access in the context of DNA data storage. Thanks for joining us Ferdinando!!

The article  “On the automorphism group of a family of maximal curves not covered by the Hermitian curve” by the algebra group member Maria Montanucci, together with co-authors Giovanni Zini (from Italy) and Guilherme Tizziotti (from Brazil) has been accepted for publication in the journal Finite Fields and Their Applications. In this article, we investigate the In this paper we compute the automorphism group of the curves introduced in Tafazolian et al. in 2016 as new examples of maximal curves which cannot be covered by the Hermitian curve. They arise as subcovers of the first generalized GK curve (GGS curve). As a result, a new characterization of the GK curve, as a member of this family, is obtained. A preprint of this article can be found here.

A new preprint on the intersection of irreducible curves and the famous Hermitian curve is now available on arXiv here.

It was written by algebra group members Peter Beelen, Maria Montanucci and Jonathan Tilling Niemann together with Mrinmoy Datta from the Indian Institute of Technology Hyderabad. The work was initiated when Mrinmoy visited the algebra group in connection with Maria’s Villum YIP project CREATE.

The 2024 IEEE International Symposium in Information Theory (ISIT 2024) will be held in person from July 7 to July 12 in Athens, Greece. The symposium covers a broad range of topics related to information theory and its connections with other areas, including but not limited to the following:

• Algebraic Aspects of Coding Theory
• Blockchains and Distributed Computing
• Coding for Computation and Storage
• Control and Information Theory
• Code Based Cryptography

Anina will give a talk on July 8th with title “A combinatorial perspective on random access efficiency for DNA storage”. Anina will also publish 2 papers on the proceedings of the symposium. They both are related to DNA storage, a very widely studied topic for its relevance in applications.

This research workshop takes place at IMPA (Rio de Janeiro, Brazil) on July 07 – 12 July 2024 and aims to bring together women and underrepresented minorities in mathematics, both from Brazil and abroad, to carry out joint research on Finite Fields and Coding Theory. Maria participates as a group leader (together with Luciane Quoos and Maria Chara) of the project ” Linear Complementary dual codes“. Together with Maria, two Master students from DTU (Johanne Müller Vistisen and Rikke Schjeldrup Jessen) attend the workshop as well. A great opportunity to meet new brilliant researchers from all over the world!

The workshop WAIFI 2024 takes place in Ottawa, Canada, during June 10-12 2024. This event is a forum of mathematicians, computer scientists, engineers and physicists performing research on finite field arithmetic, interested in communicating the advances in the theory, applications, and implementations of finite fields. Maria participates as invited plenary speaker to the event, giving the talk “Algebraic curves over finite fields: rational points and birational invariants”.

On May 24 Maria gives an invited talk for the seminar series in Number Theory at the Mathematical Institute of Bordeaux (France).

More information about the seminar series can be found at the following link.

The algebra group is happy to host Professor Luciane Quoos from the Federal University of Rio de Janeiro as a guest in the period January 3– January 17. Maria and Luciane have worked already together in the past on maximal curves, AG codes and Locally recoverable codes.

During her stay, Luciane will work with Jonathan, Peter and Maria on a class of non-isomorphic maximal curves.

Maria has accepted to become member of the editorial board of the Elsevier journal “Journal of Computational algebra”. The Journal of Computational Algebra publishes novel research about computation in, and with, algebraic or discrete structures, such that both mathematics and algorithms contribute to the new result.