{"paper":{"title":"A database of constructions of Hadamard matrices","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Dmitrii V. Pasechnik, Matteo Cati","submitted_at":"2024-11-28T04:12:50Z","abstract_excerpt":"Hadamard matrices of order $n$ are conjectured to exist whenever $n$ is $1$, $2$, or a multiple of $4$; a similar conjecture exists for skew Hadamard matrices. We provide constructions covering orders $\\le 1208$ of all known Hadamard and skew Hadamard matrices in the open-source software SageMath. This allowed us to verify the correctness of results given in the literature. Within this range, just one order, $292$, of a skew Hadamard matrix claimed to have a known construction, required a fix.\n  We also produce the up to date tables, for $n \\le 2999$ (resp. $n\\le 999$ for skew case), of the mi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18897","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.18897/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}