2015/02/14 by Bryan S. Hernandez, Hernandez, Bryan, Virgilio P. Sıson +1
Computer Science · Engineering · #94B05 #94B65 #Advanced Wireless Communication Technologies #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.1502.04210
openalex publication_date 2015/02/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Let p be a prime such that p ≡ 2 or 3 mod 5. Linear block codes over the non-commutative matrix ring of 2 × 2 matrices over the prime field GF(p) endowed with the Bachoc weight are derived as isometric images of linear block codes over the Galois field GF(p2) endowed with the Hamming metric. When seen as rank metric codes, this family of matrix codes satisfies the Singleton bound and thus are maximum rank distance codes, which are then lifted to form a special class of subspace codes, the Grassmannian codes, that meet the anticode bound. These so-called anticode-optimal Grassmannian codes are associated in some way with complete graphs. New examples of these maximum rank distance codes and anticode-optimal Grassmannian codes are given.