What’s New

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!

Today a new postdoc will start in the algebra group: Anina Gruica. Anina very recently obtained her PhD degree at the university of Eindhoven in April 2024. Nonetheless, she already has five published journal papers and four conference papers (more details can be found here here).

During her two-years postdoc, Anina will work on rank-metric codes, a type of codes studied in connection to data-transmission over networks. Anina’s postdoc is financed by Maria’s Villum YIP project CREATE. Welcome to the group Anina!

The algebra group is happy to host Associate Professor Vincent Neiger from the Université de Sorbonne as a guest in the period June 19 – July 4. Vincent has visited DTU before in 2022 and actually has been a postdoc of the algebra group before that in 2017.

Vincent will work with Peter and Maria on further improvements on the decoding of algebraic geometry codes.

Jonathan and Peter participated in the conference Combinatorics 2024 (June 3-7), which took place in Carovigno, Italy. Both gave well received talks, Peter as invited plenary speaker, Jonathan as contributing speaker. It was wonderful to participate in this great conference.

More information about the talks and the participants can be found here. A link to the slides of Peter’s talk is given here and of Jonathan’s talk here.

On May 30, Peter gave an invited talk at the Arctic University of Norway (Tromsø) in connection with a meeting of the Nordic Number theory Network. The topic of the talk was algebraic curves over finite fields with many rational points.