Paper on equivalence and characterizations of linear rank-metric codes accepted

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.

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]

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.

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.