{"paper":{"title":"Solution to an isotopism question concerning rank 2 semifields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Giuseppe Marino, Michel Lavrauw, Olga Polverino, Rocco Trombetti","submitted_at":"2013-05-19T09:19:55Z","abstract_excerpt":"In [U. Dempwolff: More Translation Planes and Semifields from Dembowski-Ostrom Polynomials, Designs, Codes, Cryptogr. \\textbf{68} (1-3) (2013), 81-103], the author gives a construction of three classes of rank two semifields of order $q^{2n}$, with $q$ and $n$ odd, using Dembowski-Ostrom polynomials. The question whether these semifields are new, i.e. not isotopic to previous constructions, is left as an open problem. In this paper we solve this problem for $n>3$, in particular we prove that two of these classes, labeled $D_{A}$ and $D_{AB}$, are new for $n>3$, whereas presemifields in family "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4342","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"}