{"paper":{"title":"On linear balancing sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.IT"],"primary_cat":"cs.IT","authors_text":"Arya Mazumdar, Pascal O. Vontobel, Ron M. Roth","submitted_at":"2009-01-21T05:22:03Z","abstract_excerpt":"Let n be an even positive integer and F be the field \\GF(2). A word in F^n is called balanced if its Hamming weight is n/2. A subset C \\subseteq F^n$ is called a balancing set if for every word y \\in F^n there is a word x \\in C such that y + x is balanced. It is shown that most linear subspaces of F^n of dimension slightly larger than 3/2\\log_2(n) are balancing sets. A generalization of this result to linear subspaces that are \"almost balancing\" is also presented. On the other hand, it is shown that the problem of deciding whether a given set of vectors in F^n spans a balancing set, is NP-hard"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.3170","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"}