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.
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:
“Generic Decoding in the Sum-Rank Metric”, Sven Puchinger, Julian Renner, Johan Rosenkilde [arXiv]
“Partial MDS Codes with Local Regeneration”, Lukas Holzbaur, Sven Puchinger, Eitan Yaakobi, Antonia Wachter-Zeh [arXiv]
“Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Powers”, Julian Renner, Sven Puchinger, Antonia Wachter-Zeh, Camilla Hollanti, Ragnar Freij-Hollanti [arXiv]
“On the Gap between Scalar and Vector Solutions of Generalized Combination Networks”, Hedongliang Liu, Hengjia Wei, Sven Puchinger, Antonia Wachter-Zeh, Moshe Schwartz [arXiv]
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.
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.
Peter Beelen participated in the biannual AGCT conference (10-14 June 2019) in CIRM, Luminy, France. The initials of this conference refer to Arithmetic, Geometry, Cryptography and Coding Theory. Invited researchers from all over the world meet in this conference to discuss recent developments on the interplay of arithmetic, geometry and their applications in cryptography and coding theory. The conference center is located near the famous Calanques, a natural park near the coast of the Mediterranean sea.
On the 20-22 May, a workshop organized by Nurdagül Anbar, Alp Bassa, Peter Beelen and Sudhir Ghorpade took place at Bogazici University and Sabanci University, Istanbul, Turkey. The topic of the workshop was polynomials and curves over finite fields. From the algebra group, apart from Peter, Maria Montanucci and Prasant Singh participated .