{"paper":{"title":"List Decoding of Lifted Gabidulin Codes via the Pl\\\"ucker Embedding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Anna-Lena Trautmann, Joachim Rosenthal, Natalia Silberstein","submitted_at":"2013-01-10T15:43:04Z","abstract_excerpt":"Codes in the Grassmannian have recently found an application in random network coding. All the codewords in such codes are subspaces of $\\F_q^n$ with a given dimension.\n  In this paper, we consider the problem of list decoding of a certain family of codes in the Grassmannian, called lifted Gabidulin codes.\n  For this purpose we use the Pl\\\"ucker embedding of the Grassmannian. We describe a way of representing a subset of the Pl\\\"ucker coordinates of lifted Gabidulin codes as linear block codes. The union of the parity-check equations of these block codes and the equations which arise from the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2165","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"}