{"paper":{"title":"On kernels and nuclei of rank metric codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Guglielmo Lunardon, Rocco Trombetti, Yue Zhou","submitted_at":"2016-06-08T13:15:36Z","abstract_excerpt":"For each rank metric code $\\mathcal{C}\\subseteq \\mathbb{K}^{m\\times n}$, we associate a translation structure, the kernel of which is shown to be invariant with respect to the equivalence on rank metric codes. When $\\mathcal{C}$ is $\\mathbb{K}$-linear, we also propose and investigate other two invariants called its middle nucleus and right nucleus. When $\\mathbb{K}$ is a finite field $\\mathbb{F}_q$ and $\\mathcal{C}$ is a maximum rank distance code with minimum distance $d<\\min\\{m,n\\}$ or $\\gcd(m,n)=1$, the kernel of the associated translation structure is proved to be $\\mathbb{F}_q$. Furthermo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02541","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"}