{"paper":{"title":"Linear Index Coding via Graph Homomorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.IT"],"primary_cat":"cs.IT","authors_text":"Javad B. Ebrahimi, Mahdi Jafari Siavoshani","submitted_at":"2014-10-06T13:47:03Z","abstract_excerpt":"It is known that the minimum broadcast rate of a linear index code over $\\mathbb{F}_q$ is equal to the $minrank_q$ of the underlying digraph. In [3] it is proved that for $\\mathbb{F}_2$ and any positive integer $k$, $minrank_q(G)\\leq k$ iff there exists a homomorphism from the complement of the graph $G$ to the complement of a particular undirected graph family called \"graph family $\\{G_k\\}$\". As observed in [2], by combining these two results one can relate the linear index coding problem of undirected graphs to the graph homomorphism problem. In [4], a direct connection between linear index "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1371","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}