2019/11/02 by Pranab Basu, Basu, Pranab, Navin Kashyap +1
Computer Science · Engineering · Mathematics · #03G10 #06B35 #Coding theory and cryptography #Combinatorics (math.CO) #Cooperative Communication and Network Coding #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #cs.DM #cs.IT #graph theory and CDMA systems #math.CO #math.IT #msc:03G10 #msc:06B35
paper · pdf · doi:10.48550/arxiv.1911.00721
24 pages, submitted to Linear Algebra and Its Applications
arxiv created 2019/11/02 · openalex publication_date 2019/11/02 · arxiv updated 2019/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The projective space ℙq(n), i.e. the set of all subspaces of the vector space \mathbbFqn, is a metric space endowed with the subspace distance metric. Braun, Etzion and Vardy argued that codes in a projective space are analogous to binary block codes in \mathbbF2n using a framework of lattices. They defined linear codes in ℙq(n) by mimicking key features of linear codes in the Hamming space \mathbbF2n. In this paper, we prove that a linear code in a projective space forms a sublattice of the corresponding projective lattice if and only if the code is closed under intersection. The sublattice thus formed is geometric distributive. We also present an application of this lattice-theoretic characterization.