{"paper":{"title":"A new family of MRD codes in $\\mathbb F_q^{2n\\times2n}$ with right and middle nuclei $\\mathbb F_{q^n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Rocco Trombetti, Yue Zhou","submitted_at":"2017-09-12T15:25:05Z","abstract_excerpt":"In this paper, we present a new family of maximum rank distance (MRD for short) codes in $\\mathbb F_{q}^{2n\\times 2n}$ of minimum distance $2\\leq d\\leq 2n$. In particular, when $d=2n$, we can show that the corresponding semifield is exactly a Hughes-Kleinfeld semifield. The middle and right nuclei of these MRD codes are both equal to $\\mathbb F_{q^n}$. We also prove that the MRD codes of minimum distance $2<d<2n$ in this family are inequivalent to all known ones. The equivalence between any two members of this new family is also determined."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03908","kind":"arxiv","version":2},"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"}