{"paper":{"title":"Construction of full diversity $D_n$-lattices for all $n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Grasiele C. Jorge, Robson R. de Araujo","submitted_at":"2017-09-16T16:13:25Z","abstract_excerpt":"In this paper we construct some families of rotated $D_n$-lattices with full diversity for any $n$. These lattices can be good for signal transmission over both Gaussian and Rayleigh fading channels. In order to get bounds for their minimum product distances, we show that the $Z$-modules used in \\cite{sethoggier} to obtain rotated $\\mathbb{Z}^{n}$-lattices with $n$ odd are ideals and find a sufficient condition for such ideals being principal ideals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05536","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"}