{"paper":{"title":"A Note on \"On the Construction of Boolean Functions with Optimal Algebraic Immunity\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CR","authors_text":"Futatsugi Kokichi, Haibin Kan, Yuan Li","submitted_at":"2011-10-18T05:09:36Z","abstract_excerpt":"In this note, we go further on the \"basis exchange\" idea presented in \\cite{LiNa1} by using Mobious inversion. We show that the matrix $S_1(f)S_0(f)^{-1}$ has a nice form when $f$ is chosen to be the majority function, where $S_1(f)$ is the matrix with row vectors $\\upsilon_k(\\alpha)$ for all $\\alpha \\in 1_f$ and $S_0(f)=S_1(f\\oplus1)$. And an exact counting for Boolean functions with maximum algebraic immunity by exchanging one point in on-set with one point in off-set of the majority function is given. Furthermore, we present a necessary condition according to weight distribution for Boolean"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3876","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"}