2024/06/18 by Usman Mushrraf, Ferdinando Zullo, Mushrraf, Usman +1 · 2 citations
Computer Science · Engineering · #Advanced Wireless Network Optimization #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2406.12450
openalex publication_date 2024/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Symq(m) be the space of symmetric matrices in \mathbbFqm× m. A subspace of Symq(m) equipped with the rank distance is called a symmetric rank-metric code. In this paper we study the covering properties of symmetric rank-metric codes. First we characterize symmetric rank-metric codes which are perfect, i.e. that satisfy the equality in the sphere-packing like bound. We show that, despite the rank-metric case, there are non trivial perfect codes. Also, we characterize families of codes which are quasi-perfect.