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Ph.D. student Grigory Solomatov defends his thesis

Peter Beelen No Comments

Today, Grigory defended his Ph.D. thesis successfully! After giving an excellent presentation on his work, he answered various questions from his opponents. During his Ph.D. Grigory obtained various results on computational aspects of algebraic geometry (AG) codes, including results on encoding and decoding such codes. The results include decoding any AG code very efficiently, matching and very often improving preexisting decoders.

We would like to acknowledge the support from The Danish Council for Independent Research (DFF-FNU) for the project Correcting on a Curve, Grant No. 8021-00030B. Their support made Grigory’s Ph.D. project and the obtained results a reality.

Congratulations to Grigory with obtaining his Ph.D.-degree!

Paper appears in Finite Fields and Their Applications

Maria Montanucci No Comments

The paper “A class of linear sets in PG(1,q^5)” by Maria and Corrado Zanella appeared online in the journal Finite Fields and its Applications. In the manuscript Maria and Corrado study some interesting combinatorial structures called maximum scattered linear sets over projective spaces. These structures have been intensively studied during the last year, particularly for the connection to coding theory (MRD codes).

Maximum scattered linear sets over PG(1,q^n) have been completely classified for n at most 4 by Csajbók-Zanella (2018) and Lavrauw-Van de Voorde (2010). In this paper Maria and Corrado analyze the case n=5. There a wide class of linear sets is studied which depends on two parameters. Conditions for the existence, in this class, of possible new maximum scattered linear sets in are exhibited.

Paper published in Advances in Geometry

Maria Montanucci No Comments

The paper “An Fp2-maximal Wiman’s sextic and its automorphisms” by Maria, Massimo Giulietti, Motoko Kawakita and Stefano Lia appeared online in the journal Advances in Geometry. In this paper Maria, Massimo, Motoko and Stefano study a sextic curve introduced in 1895 by Wiman as a Riemann surface over the complex field, but seen over finite fields. They showed that its full automorphism group is isomorphic to the symmetric group S5, generalizing Wiman’s result. It is also shown that when the finite field has cardinality 19^2 then the Wiman’s sextic is maximal and it is not Galois covered by the Hermitian curve.

PhD-student Grigory Solomatov hands in his thesis

Peter Beelen No Comments

Yesterday, Grigory Solomatov handed in his PhD thesis “Computational Aspects of Algebraic Geometry Codes”. We would like to congratulate Grigory with this! His PhD defense is planned to take place on the 16th of December.

Grigory’s PhD was financed by the DFF-FNU project “Correcting on a curve”. Grigory will stick around a bit longer, since it was possible to hire him as a research assistant till the end of the year.

Maria becomes editor of JCTA

Maria Montanucci No Comments

Maria has accepted to become editor of the Elsevier journal “Journal of Combinatorial Theory Series A” for the next 3 years. The Journal of Combinatorial Theory, Series A is one of the premier journals on theoretical and practical aspects of combinatorics in all branches of science. The journal is primarily concerned with finite and discrete structures, designs, finite geometries, codes, combinatorics with number theory, combinatorial games, extremal combinatorics, combinatorics of storage, and other important theory/applications of combinatorics.

Paper accepted in Linear Algebra and its Applications

Maria Montanucci No Comments

Today Maria’s paper “On a conjecture about maximum scattered subspaces of Fq6×Fq6” appeared online in Linear Algebra and its Applications, as a joint work with Daniele Bartoli and Bence Csajbók. Here Bence, Daniele and Maria proved a conjecture from 2018 regarding a family of maximum scattered subspaces of Fq6 x Fq6. A preprint is available here.

SIAM AG 2021

Maria Montanucci No Comments

Today, Maria gave a talk for the online conference SIAM Conference on Applied Algebraic Geometry (AG21). Her talk, titled “Error correcting codes from maximal curves”, was a part of the mini-symposium Polynomial and Evaluation Codes and their Applications. In her talk Maria presented several construction of error correcting codes (AG codes, quantum codes and locally recoverable codes) using the nice structure of automorphism groups of maximal curves.

Paper appeared online in FFA

Peter Beelen No Comments

The paper “Point-line incidence on Grassmannians and majority logic decoding of Grassmann codes” by Peter and Prasant Singh appeared online in the journal Finite Fields and Their Applications. In this paper Peter and Prasant, a former postdoc of the algebra group, explain how to use the subtle structure of lines on Grassmannians to correct errors using Grassmann codes with an old technique called majority logic decoding. The result is a fast decoding algorithm for Grassmann codes.

Paper published in Advances in Geometry

Maria Montanucci No Comments

Today, Maria’s paper “Fp2-maximal curves with many automorphisms are Galois-covered by the Hermitian curve” appeared in the journal Advances in Geometry, as a joint work with Daniele Bartoli and Fernando Torres. Here a open problem dated 2000 is analyzed. Namely, is it true that every Fp2-maximal curve (where p is a prime) is covered by the Hermitian curve? In this paper Maria, Daniele and Fernando show that this is the case provided that the curve has a sufficiently large automorphism group. Also, the first example of an Fp2-maximal curve which is not Galois-covered by the Hermitian curve is presented. A preprint is available here.

Paper published in FFA

Maria Montanucci No Comments

Peter, Maria and Leonardo’s paper “Weierstrass semigroups on the Skabelund maximal curve” has been accepted for publication in the journal Finite Fields and their Applications. Here the Weierstrass semigroup is computed at every point of the Skabelund maximal curve (covering the famous Suzuki curve), as well as the Weierstrass points of the curve. Since these are the main ingredients to construct AG codes, the result has interesting consequence in applications. Also, this is one of the few examples in the literature in which this complete analysis is known. A preprint is available here.