{"paper":{"title":"Linear Codes from Projective Linear Anticodes Revisited","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Conghui Xie, Hao Chen","submitted_at":"2024-06-11T09:55:57Z","abstract_excerpt":"An anticode ${\\bf C} \\subset {\\bf F}_q^n$ with the diameter $\\delta$ is a code in ${\\bf F}_q^n$ such that the distance between any two distinct codewords in ${\\bf C}$ is at most $\\delta$. The famous Erd\\\"{o}s-Kleitman bound for a binary anticode ${\\bf C}$ of the length $n$ and the diameter $\\delta$ asserts that $$|{\\bf C}| \\leq \\Sigma_{i=0}^{\\frac{\\delta}{2}} \\displaystyle{n \\choose i}.$$ In this paper, we give an antiGriesmer bound for $q$-ary projective linear anticodes, which is stronger than the above Erd\\\"{o}s-Kleitman bound for binary anticodes. The antiGriesmer bound is a lower bound on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.07112","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/2406.07112/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"}