{"paper":{"title":"Simultaneous Rational Function Codes: Improved Analysis Beyond Half the Minimum Distance with Multiplicities and Poles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SC","math.IT"],"primary_cat":"cs.IT","authors_text":"Eleonora Guerrini, Matteo Abbondati, Romain Lebreton","submitted_at":"2025-08-07T11:28:44Z","abstract_excerpt":"In this paper, we extend the work of Abbondati et al. (2024) on decoding simultaneous rational function codes by addressing two important scenarios: multiplicities and poles (zeros of denominators). First, we generalize previous results to rational codes with multiplicities by considering evaluations with multi-precision. Then, using the hybrid model from Guerrini et al. (2023), we extend our approach to vectors of rational functions that may present poles. Our contributions include: a rigorous analysis of the decoding algorithm's failure probability that generalizes and improves several previ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.05284","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/2508.05284/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"}