{"paper":{"title":"A lower bound on the average entropy of a function determined up to a diagonal linear map on F_q^n","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Ram Zamir, Yaron Shany","submitted_at":"2011-05-19T05:28:05Z","abstract_excerpt":"In this note, it is shown that if $f\\colon\\efq^n\\to\\efq^n$ is any function and $\\bA=(A_1,..., A_n)$ is uniformly distributed over $\\efq^n$, then the average over $(k_1,...,k_n)\\in \\efq^n$ of the Renyi (and hence, of the Shannon) entropy of $f(\\bA)+(k_1A_1,...,k_nA_n)$ is at least about $\\log_2(q^n)-n$. In fact, it is shown that the average collision probability of $f(\\bA)+(k_1A_1,...,k_nA_n)$ is at most about $2^n/q^n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3793","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"}