2025/09/22 by Edyta Bartnicka, Bartnicka, Edyta
Computer Science · Engineering · #Coding theory and cryptography #graph theory and CDMA systems #Quantum Computing Algorithms and Architecture
paper · pdf · doi:10.48550/arxiv.2509.17958
Let Γk(V) be the Grassmann graph whose vertex set \mathcal Gk(V) is formed by all k-dimensional subspaces of an n-dimensional vector space V over the finite field Fq consisting of q elements. Denote by Π[n,k]q the subgraph of Γk(V) formed by projective codes. We give a complete description of cliques ⟨ U]Πk of Π[n,k]q consisting of all k-dimensional projective codes contained in a fixed (k+1)-dimensional subspace of V. We show when and in how many lines of \mathcal Gk(V) they are contained. Next we prove that ⟨ U]Πk is a maximal clique of Π[n,k]q exactly if it is contained in at most one line of \mathcal Gk(V).