{"paper":{"title":"Reconstruction Codes for Deletions and Insertions: Connection, Distinction, and Construction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Gennian Ge, Yubo Sun","submitted_at":"2025-08-20T03:26:55Z","abstract_excerpt":"Let $\\mathcal{B}(\\cdot)$ be an error ball function. A set of $q$-ary sequences of length $n$ is referred to as an \\emph{$(n,q,N;\\mathcal{B})$-reconstruction code} if each sequence $\\boldsymbol{x}$ within this set can be uniquely reconstructed from any $N$ distinct elements within its error ball $\\mathcal{B}(\\boldsymbol{x})$. The main objective in this area is to determine or establish bounds for the minimum redundancy of $(n,q,N;\\mathcal{B})$-reconstruction codes, denoted by $\\rho(n,q,N;\\mathcal{B})$. In this paper, we investigate reconstruction codes where the error ball is either the \\emph{$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.14386","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/2508.14386/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"}