{"paper":{"title":"Typical sumsets of linear codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Jingge Zhu, Michael Gastpar","submitted_at":"2015-11-26T16:01:19Z","abstract_excerpt":"Given two identical linear codes $\\mathcal C$ over $\\mathbb F_q$ of length $n$, we independently pick one codeword from each codebook uniformly at random. A $\\textit{sumset}$ is formed by adding these two codewords entry-wise as integer vectors and a sumset is called $\\textit{typical}$, if the sum falls inside this set with high probability. We ask the question: how large is the typical sumset for most codes? In this paper we characterize the asymptotic size of such typical sumset. We show that when the rate $R$ of the linear code is below a certain threshold $D$, the typical sumset size is ro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08435","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":""},"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"}