{"paper":{"title":"Constructing and Counting Even-Variable Symmetric Boolean Functions with Algebraic Immunity not Less Than $d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CR","authors_text":"Haibin Kan, Hui Wang, Yuan Li","submitted_at":"2011-10-18T05:00:29Z","abstract_excerpt":"In this paper, we explicitly construct a large class of symmetric Boolean functions on $2k$ variables with algebraic immunity not less than $d$, where integer $k$ is given arbitrarily and $d$ is a given suffix of $k$ in binary representation. If let $d = k$, our constructed functions achieve the maximum algebraic immunity. Remarkably, $2^{\\lfloor \\log_2{k} \\rfloor + 2}$ symmetric Boolean functions on $2k$ variables with maximum algebraic immunity are constructed, which is much more than the previous constructions. Based on our construction, a lower bound of symmetric Boolean functions with alg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3875","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":""},"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"}