{"paper":{"title":"Discrete Fourier Transform Approach to Cyclically Covering Subspaces of $\\mathbb{F}^n_q$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Pingzhi Yuan, Yangcheng Li","submitted_at":"2026-06-11T13:04:23Z","abstract_excerpt":"Let $q$ be a prime power and $n$ a positive integer. A subspace \\( U \\subseteq \\mathbb{F}_q^n \\) is called cyclically covering if the union of all its cyclic shifts covers the whole space \\( \\mathbb{F}_q^n \\). Let \\( h_q(n) \\) denote the maximum possible codimension of such a subspace. When \\(\\gcd(q,n)=1\\), we derive necessary and sufficient conditions for \\(h_q(n)=0\\) via Discrete Fourier Transforms, and prove this equality is equivalent to the existence of full-weight codewords in cyclic codes of \\(\\mathbb{F}_q^n\\). We also characterize codimension-$k$ cyclically covering subspaces.\n  Based "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13307","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.13307/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}