{"paper":{"title":"Few-cosine spherical codes and Barnes-Wall lattices","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"jr, Robert L. Griess","submitted_at":"2006-05-07T11:01:23Z","abstract_excerpt":"Using Barnes-Wall lattices and 1-cocycles on finite groups of monomial matrices, we give a procedure to construct tricosine spherical codes. This was inspired by a 14-dimensional code which Ballinger, Cohn, Giansiracusa and Morris discovered in studies of the universally optimal property. It has 64 vectors and cosines $-3/7, -1/7, 1/7$. We construct the {\\it Optimism Code}, a 4-cosine spherical code with 256 unit vectors in 16-dimensions. The cosines are $0, 1/4, -1/4, -1$. Its automorphism group has shape $2^{1+8}{\\cdot}GL(4,2)$. The Optimism Code contains a subcode related to the BCGM code. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605175","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"}