2022/01/20 by Daniele Bartoli, Bartoli, Daniele, Giovanni Zini +3
Computer Science · Mathematics · #Algebraic structures and combinatorial models #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2201.08242
openalex publication_date 2022/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The tensor rank of some Gabidulin codes of small dimension is investigated. In particular, we determine the tensor rank of any rank metric code equivalent to an 8-dimensional \mathbbFq-linear generalized Gabidulin code in \mathbbFq4×4. This shows that such a code is never minimum tensor rank. In this way, we detect the first infinite family of Gabidulin codes which are not minimum tensor rank.