{"paper":{"title":"Generalized Fano and non-Fano networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Brijesh Kumar Rai, Niladri Das","submitted_at":"2016-09-19T16:24:06Z","abstract_excerpt":"It is known that the Fano network has a vector linear solution if and only if the characteristic of the finite field is $2$; and the non-Fano network has a vector linear solution if and only if the characteristic of the finite field is not $2$. Using these properties of Fano and non-Fano networks it has been shown that linear network coding is insufficient. In this paper we generalize the properties of Fano and non-Fano networks. Specifically, by adding more nodes and edges to the Fano network, we construct a network which has a vector linear solution for any vector dimension if and only if th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05815","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"}