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.
Maria’s paper “MRD-codes arising from the trinomial xq+xq3+cxq5∈Fq6[x]” with co-authors Ferdinando Zullo and Giuseppe Marino has been accepted for publication in the journal Linear Algebra and its Applications. Here, using algebraic curves over finite fields, a new family of maximum rank distance codes (MRD) has been constructed. A preprint is available here.
Maria and Gabor Korchmaros (Maria’s former PhD supervisor) published their paper “Large odd prime power order automorphism groups of algebraic curves in any characteristic” in Journal of Algebra. There sharp upper bounds for the order of prime power order automorphism groups of algebraic curves are obtained. Also, a recursive way to construct extremal examples is proposed, using elliptic curves. A preprint is available here.
Today Maria’s paper “Large automorphism groups of ordinary curves of even genus in odd characteristic” has been accepted in Communications in Algebra. This is a joint work with Pietro Speziali and gives strong upper bound for the size of the automorphism group of ordinary curves (that is, when genus and p-rank coincide) of even genus, with respect to the genus itself. A preprint is available here.
Maria and Giovanni Zini are happy to share the news that their joint paper “Quotients of the Hermitian curve from subgroups of PGU(3,q) without fixed points or triangles” has been accepted for publication in the Journal of Algebraic Combinatorics. There the genera of quotients of the Hermitian curve from semiregular subgroups of PGU(3,q) (that is, fixing neither points nor triangles in the plane) are computed. A preprint can be found here.