2025/05/13 by Duy Ho, Ho, Duy, Trygve Johnsen +1
Computer Science · Engineering · Mathematics · #94B05 #94B25 #94B60 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Information Theory (cs.IT) #graph theory and CDMA systems
paper · doi:10.48550/arxiv.2505.08506
openalex publication_date 2025/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The intersection of a linear code with its dual is called the hull of the code. It is known that, for classical linear codes under the Hamming-metric, the dimension of the hull can be reduced up to equivalence. This phenomenon leads to the so-called hull-variation problem formulated by Hao Chen in 2023. In this paper, we consider the analogous problem for vector rank-metric codes, along with their associated matrix codes and extended block codes. Our results include the fact that every vector rank-metric code over any finite field \mathbbFq, in particular when q=2 or q=3, is equivalent to an LCD code.