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.
Maria’s paper “On plane curves given by separated polynomials and their automorphisms” (joint work with Giovanni Zini and Matteo Bonini) appeared in Advances in Geometry. Here the automorphism group of curves of type A(x)=B(y), where A has degree prime to p and B is a linearized polynomial is computed over finite fields of characteristic p. A preprint can be found here.
Maria’s joint work with Pietro Speziali “Large automorphism groups of ordinary curves in characteristic 2” has been accepted for publication in Journal of Algebra. There sharp upper bound for the size of automorphism groups of ordinary curves in characteristic 2 are provided. A similar answer is given simultaneously in another joint paper of Maria with her former PhD supervisor Gabor Korchmaros in odd characteristic.
Maria, Giovanni Zini and Francesca Dalla Volta published their joint paper “On the classification problem for the genera of quotients of the Hermitian curve” in Communications in Algebra. There some open problems regarding the complete classification of genera of quotients of the Hermitian curve are listed and solved. A preprint is available here.