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.
Postdoc Sven Puchinger with co-authors from TU Munich (Julian Renner and Antonia Wachter-Zeh), German Aerospace Center (Thomas Jerkovits and Hannes Bartz), and Université de Rennes 1 (Pierre Loidreau) got a paper accepted at the International Conference on Post-Quantum Cryptography (PQCrypto) 2020:
“Randomized Decoding of Gabidulin Codes Beyond the Unique Decoding Radius”, Julian Renner, Thomas Jerkovits, Hannes Bartz, Sven Puchinger, Pierre Loidreau, Antonia Wachter-Zeh [link] [arXiv]
The paper proposes a significantly faster algorithm to solve a decoding problem which the security of three code-based cryptosystems is based on.
In the period January 6-17, Peter visited Tromsø (Norway), where the Arctic University of Norway is located. His host, Prof. Trygve Johnsen has visited the algebra group in the past during his sabattical. During Peter’s visit, he finished two papers and initiated a new one, so the visit was very productive!
The Algebra group was visited by Julian Renner for one week in November 2019. Julian is a PhD student at TU Munich and has published several papers with postdoc Sven Puchinger.
During the visit, Johan, Sven, and Julian worked on generic decoding in the sum-rank metric and on low-rank parity-check codes over finite rings. Julian also gave a very nice talk on “Key Compression for Rank-Based Cryptosystems” in the algebra group colloquium.
Update: The visit resulted in two papers accepted at ISIT 2020.
The Algebra group has a great new addition: Postdoc Sven Puchinger started 1st October on his 2-year H. C. Ørsted fellowship. Sven Puchinger has his PhD Degree from the University of Ulm under the supervision of Martin Bossert (where Johan was also a postdoc in 2014-2015), and he spent the last 1,5 years as a postdoc at Technical University of Munich.
His research interests are broadly within algebraic coding theory, from new code constructions to decoding and fancy applications. Sven already has numerous joint papers with Johan and Peter, and we foresee that his postdoc here will be very fruitful.
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.
Grigory and Leonardo created this great cartoon explaining the principles and importance of coding theory – illustrated by a cross-galactic love story!
The video was made as their contribution to the DTU Compute PhD Bazaar.
Enjoy:
Peter and Grigory participated in the workshop MWCC in the period July 15-16. In this workshop experts from all over the world shared their latest insights on codes and their applications in cryptography. Peter gave a talk on his work with postdoc Prasant Singh on the decoding of codes from Grassmann varieties. Grigory presented a poster on the fast encoding of AG codes.
Johan and Grigory participated in the conference SIAM Applied Algebraic Geometry 2019. The conference had many talks on computer algebra, coding theory and cryptography. Johan gave a talk entitled “Decoding of Gabidulin codes and friends using row reduction of skew polynomial matrices”.
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.