Paper appeared in Designs, Codes and Cryptography

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.

Today Maria gave a seminar for the online seminar series “Galois geometries and their application”, organized by Olga Polverino, Ferdinando Zullo and Giovanni Zini (University of Campania, Caserta). The title of her seminar was “Maximal curves over finite fields” and the slide are available here. The webpage of the conference can be found at this link.

Today Maria’s joint work with Daniele Bartoli and Luciane Quoos “Locally recoverable codes from automorphism groups of function fields of genus g>=1” appeared in the journal IEEE Transactions on Information Theory. Here locally recoverable codes from function fields of genus at least 1 are constructed and a new Singleton-like bound for locally recoverable codes with multiple recovering sets is obtained. A preprint can be found here.

Today Maria and Peter published their paper “On subfields of the second generalization of the GK maximal function field” in Finite Fields and their Applications. Here several new maximal curves are constructed corresponding to subfields of the second generalized GK maximal curve. A preprint can be found here.

Maria and Giovanni Zini published their joint paper “The complete list of genera of quotients of the Fq2-maximal Hermitian curve for q≡1 (mod 4)” in Journal of Algebra. Here an open problem from 2000 is partially solved, namely that of computing all the genera of quotients of the Hermitian curve over Fq2, q prime power. Indeed such a complete list of genera is obtained here if q is congruent to 1 modulo 4. A preprint can be found here.

Today’s Maria joint work with Vincenzo Pallozzi Lavorante “AG codes from the second generalization of the GK maximal curve” appeared in the journal Discrete Mathematics. Here Weierstrass semigroups and points on the second generalized GK curve are computed, as well as, some AG codes (and AG quantum codes) with new and good parameters. A preprint is available here.