{"paper":{"title":"Sequences of LCD AG codes and LCP of AG Codes attaining the Tsfasman-Vladut-Zink bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.AG","authors_text":"Adler Marques, Luciane Quoos","submitted_at":"2025-05-29T18:39:37Z","abstract_excerpt":"Since Massey introduced linear complementary dual (LCD) codes in 1992 and Bhasin et al. later formalized linear complementary pairs (LCPs) of codes - structures with important cryptographic applications - these code families have attracted significant interest. We construct infinite sequences $(C_i)_{i \\geq 1}$ of LCD codes and of LCPs $(C', D')_{i \\geq 1}$ over $\\mathbb{F}_{q^2}$ obtained from the Garcia-Stichtenoth tower of function fields, where we describe suitable non-special divisors of small degree on each level of the tower. These families attain the Tsfasman-Vl\\u{a}du\\c{t}-Zink bound "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.23937","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/2505.23937/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"}