{"paper":{"title":"Upper Bounds on Matching Families in $\\mathbb{Z}_{pq}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Huaxiong Wang, Liang Feng Zhang, San Ling, Yeow Meng Chee","submitted_at":"2013-01-06T06:54:44Z","abstract_excerpt":"\\textit{Matching families} are one of the major ingredients in the construction of {\\em locally decodable codes} (LDCs) and the best known constructions of LDCs with a constant number of queries are based on matching families. The determination of the largest size of any matching family in $\\mathbb{Z}_m^n$, where $\\mathbb{Z}_m$ is the ring of integers modulo $m$, is an interesting problem. In this paper, we show an upper bound of $O((pq)^{0.625n+0.125})$ for the size of any matching family in $\\mathbb{Z}_{pq}^n$, where $p$ and $q$ are two distinct primes. Our bound is valid when $n$ is a const"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0980","kind":"arxiv","version":2},"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"}