{"paper":{"title":"A New Class of Linear Codes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT","math.NT"],"primary_cat":"cs.IT","authors_text":"Akash Bhople, Giacomo Cherubini, Giacomo Micheli, Tefjol Pllaha","submitted_at":"2024-01-15T22:14:44Z","abstract_excerpt":"Let $n$ be a prime power, $r$ be a prime with $r\\mid n-1$, and $\\varepsilon\\in (0,1/2)$. Using the theory of multiplicative character sums and superelliptic curves, we construct new codes over $\\mathbb F_r$ having length $n$, relative distance $(r-1)/r+O(n^{-\\varepsilon})$ and rate $n^{-1/2-\\varepsilon}$. When $r=2$, our binary codes have exponential size when compared to all previously known families of linear and non-linear codes with relative distance asymptotic to $1/2$, such as Delsarte--Goethals codes. Moreover, concatenating with a Reed-Solomon code we get a family of codes of length $n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.07986","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.07986/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"}