{"paper":{"title":"Extended codes and deep holes of MDS codes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Cunsheng Ding, Tingfang Chen, Yansheng Wu","submitted_at":"2023-12-09T10:55:11Z","abstract_excerpt":"For a given linear code $\\C$ of length $n$ over $\\gf(q)$ and a nonzero vector $\\bu$ in $\\gf(q)^n$, Sun, Ding and Chen defined an extended linear code $\\overline{\\C}(\\bu)$ of $\\C$, which is a generalisation of the classical extended code $\\overline{\\C}(-\\bone)$ of $\\C$ and called the second kind of an extended code of $\\C$ (see arXiv:2307.04076 and arXiv:2307.08053). They developed some general theory of the extended codes $\\overline{\\C}(\\bu)$ and studied the extended codes $\\overline{\\C}(\\bu)$ of several families of linear codes, including cyclic codes, projective two-weight codes, nonbinary H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.05534","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/2312.05534/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"}