This month, the paper “Hyperplane Sections of Determinantal Varieties over Finite Fields and Linear Codes” appeared in the September issue of the journal Discrete Mathematics. The paper is written by Peter and Prof. Sudhir Ghorpade from IIT Bombay, a regular guest of the algebra group with whom Peter has written several papers before. A preprint can be found here.
The paper “Equivalence and Characterizations of Linear Rank-Metric Codes Based on Invariants” [arXiv] by Alessandro Neri (TU Munich, Germany), group member Sven Puchinger, and Anna-Lena Horlemann-Trautmann (University of St. Gallen, Switzerland) was accepted for publication in Linear Algebra and Its Applications.
The paper studies a tool to efficiently determine the equivalence of linear rank-metric codes – a topic of growing importance due to many new code constructions in the last years. Furthermore, bounds on the number of equivalence classes of two code families and different characterizations for one code class are given.
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.
On May 28-29, Peter co-organized a workshop with Fabien Pazuki from Copenhagen University. The workshop was part of a series of activities organized by N^3 (Nordic Number theory Network, see here for more information). Though originally planned to take place at DTU, the event was held online due to the covid19 situation.
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.
Freja Elbro started a few months ago as a PhD student with Lars R. Knudsen in the Cyber Security section but is from 1st May co-advised by Johan Rosenkilde of the Algebra group.
Freja’s project is quantum-safe asymmetric cryptography based on coding theory, with a focus on McEliece-like constructions.
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.
Group members Johan Rosenkilde and Sven Puchinger, together with several co-authors from Israel, Finland, and Germany, got four papers accepted at this year’s ISIT, the IEEE flagship conference on information theory: