{"paper":{"title":"Properties of Constacyclic Codes Under the Schur Product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Brett Hemenway Falk, Michael Rudow, Nadia Heninger","submitted_at":"2018-10-17T15:46:59Z","abstract_excerpt":"For a subspace $W$ of a vector space $V$ of dimension $n$, the Schur-product space $W^{\\langle k\\rangle}$ for $k \\in \\mathbb{N}$ is defined to be the span of all vectors formed by the component-wise multiplication of $k$ vectors in $W$. It is well known that repeated applications of the Schur product to the subspace $W$ creates subspaces $W, W^{\\langle 2 \\rangle}, W^{\\langle 3 \\rangle}, \\ldots$ whose dimensions are monotonically non-decreasing. However, quantifying the structure and growth of such spaces remains an important open problem with applications to cryptography and coding theory. Thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07630","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"}