{"paper":{"title":"Capacity Analysis of Linear Operator Channels over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"En-hui Yeung, Jin Meng, Shenghao Yang, Siu-Wai Ho","submitted_at":"2011-08-22T08:55:32Z","abstract_excerpt":"Motivated by communication through a network employing linear network coding, capacities of linear operator channels (LOCs) with arbitrarily distributed transfer matrices over finite fields are studied. Both the Shannon capacity $C$ and the subspace coding capacity $C_{\\text{SS}}$ are analyzed. By establishing and comparing lower bounds on $C$ and upper bounds on $C_{\\text{SS}}$, various necessary conditions and sufficient conditions such that $C=C_{\\text{SS}}$ are obtained. A new class of LOCs such that $C=C_{\\text{SS}}$ is identified, which includes LOCs with uniform-given-rank transfer matr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4257","kind":"arxiv","version":3},"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"}