In the issue of this month of the prestigious journal IEEE Transactions on Information Theory, you can find the article “Fast Encoding of AG Codes over C_ab Curves” by Peter, Johan, and Grigory. In this article it is explained how to convert a message into a codeword (encoding) as well as the reverse process (unencoding) fast for a significant class of algebraic geometry codes. A preprint is available here.
Starting the first of March 2021 Johan left DTU for a job at GitHub as a Research Engineer. The algebra group would like to thank him for his input, energy and enthusiasm throughout the years. Best of luck with your new job!
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.
After a highly successful postdoc in the algebra group, Sven obtained a new position as a postdoc at the Technical University of Munich. We would like to thank Sven for his work in the algebra group and wish him all the best for the future!
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.
As part of the DTU outreach activities towards high schools, Peter gave a guest lecture on solving cubic polynomial equations. The activities are organized within the framework of an InterMat workshop (see https://matematicum.dtu.dk/intermat for information. Danish only). With various high school students listening online, an explanation was given on how to use Tschirnhaus transforms to obtain the famous Cardano solution formulas. The same method can be used to solve the quartic equation.
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.