Maria has accepted to become editor of the Elsevier journal “Journal of Combinatorial Theory Series A” for the next 3 years. The Journal of Combinatorial Theory, Series A is one of the premier journals on theoretical and practical aspects of combinatorics in all branches of science. The journal is primarily concerned with finite and discrete structures, designs, finite geometries, codes, combinatorics with number theory, combinatorial games, extremal combinatorics, combinatorics of storage, and other important theory/applications of combinatorics.
Today Maria’s paper “On a conjecture about maximum scattered subspaces of Fq6×Fq6” appeared online in Linear Algebra and its Applications, as a joint work with Daniele Bartoli and Bence Csajbók. Here Bence, Daniele and Maria proved a conjecture from 2018 regarding a family of maximum scattered subspaces of Fq6 x Fq6. A preprint is available here.
Today, Maria gave a talk for the online conference SIAM Conference on Applied Algebraic Geometry (AG21). Her talk, titled “Error correcting codes from maximal curves”, was a part of the mini-symposium Polynomial and Evaluation Codes and their Applications. In her talk Maria presented several construction of error correcting codes (AG codes, quantum codes and locally recoverable codes) using the nice structure of automorphism groups of maximal curves.
Today, Maria’s paper “Fp2-maximal curves with many automorphisms are Galois-covered by the Hermitian curve” appeared in the journal Advances in Geometry, as a joint work with Daniele Bartoli and Fernando Torres. Here a open problem dated 2000 is analyzed. Namely, is it true that every Fp2-maximal curve (where p is a prime) is covered by the Hermitian curve? In this paper Maria, Daniele and Fernando show that this is the case provided that the curve has a sufficiently large automorphism group. Also, the first example of an Fp2-maximal curve which is not Galois-covered by the Hermitian curve is presented. A preprint is available here.
Peter, Maria and Leonardo’s paper “Weierstrass semigroups on the Skabelund maximal curve” has been accepted for publication in the journal Finite Fields and their Applications. Here the Weierstrass semigroup is computed at every point of the Skabelund maximal curve (covering the famous Suzuki curve), as well as the Weierstrass points of the curve. Since these are the main ingredients to construct AG codes, the result has interesting consequence in applications. Also, this is one of the few examples in the literature in which this complete analysis is known. A preprint is available here.
Today Maria’s paper “On certain self-orthogonal AG codes with applications to Quantum error-correcting codes” appeared in the journal Designs, Codes and Cryptography, as a joint work with Daniele Bartoli and Giovanni Zini. Here, a construction of quantum codes from self-orthogonal algebraic geometry codes is provided as well as on a new family of algebraic curves to which the construction is applied, named Swiss curves. The reason behind this curious name, is that the authors developed the key ideas proposed in this publication during the conference SIAM AG19, which took place in Bern (Switzerland). A preprint is available here.
Maria’s joint work with Daniele Bartoli and Giovanni Zini “Weierstrass semigroup at every point of the Suzuki curve” has been accepted in Acta Arithmetica and will appear in volume 197 (2021). As the title suggests, the Weierstrass semigroup at every point of the Suzuki curve is computed, as one of the few examples in the literature in which such a complete description is available. A preprint can be found here.
Today Maria’s paper “On the classification of exceptional scattered polynomials” appears online in the Journal of Combinatorial Theory series A, and it is a joint work with Daniele Bartoli. The paper will be published in volume 179 (April 2021) and deals with the problem of classifying a special class of polynomials over finite fields, called “exceptional scattered polynomials”. A preprint is available here.
The paper “New examples of maximal curves with low genus” by Maria together with Daniele Bartoli, Massimo Giulietti and Motoko Kawakita appeared in the journal Finite Fields and their Applications. Here a method to construct maximal curves using the so-called “Kani-Rosen Theorem” is presented, resulting in new examples of maximal curves of low genus. A preprint is available here.
ACCESS (Algebraic Coding and Cryptography on the East Coast) is a recently launched online seminar series designed to highlight world-class research in coding theory, cryptography and related areas and to encourage collaboration between its participants, see here. As invited speaker, Maria gave a talk today with the title “Maximal curves over finite fields and their applications to coding theory”. The slides of the presentation are available here.