{"paper":{"title":"Weight recursions for any rotation symmetric Boolean functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Thomas W. Cusick","submitted_at":"2017-01-10T20:10:46Z","abstract_excerpt":"Let $f_n(x_1, x_2, \\ldots, x_n)$ denote the algebraic normal form (polynomial form) of a rotation symmetric Boolean function of degree $d$ in $n \\geq d$ variables and let $wt(f_n)$ denote the Hamming weight of this function. Let $(1, a_2, \\ldots, a_d)_n$ denote the function $f_n$ of degree $d$ in $n$ variables generated by the monomial $x_1x_{a_2} \\cdots x_{a_d}.$ Such a function $f_n$ is called {\\em monomial rotation symmetric} (MRS). It was proved in a $2012$ paper that for any MRS $f_n$ with $d=3,$ the sequence of weights $\\{w_k = wt(f_k):~k = 3, 4, \\ldots\\}$ satisfies a homogeneous linear "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06648","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"}