{"id":"W2231642173","doi":"10.1080/03081087.2016.1265062","title":"Generalization of Scarpis’ theorem on Hadamard matrices","year":2016,"lang":"en","type":"article","venue":"Linear and Multilinear Algebra","topic":"graph theory and CDMA systems","field":"Engineering","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Hadamard transform; Hadamard matrix; Hadamard's inequality; Hadamard's maximal determinant problem; Hadamard three-lines theorem; Hadamard product; Hadamard three-circle theorem; Complex Hadamard matrix","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001516415,0.0001301731,0.0001700846,0.00008740973,0.00003379306,0.00000909918,0.00008136828,0.00008016055,0.00005298023],"category_scores_gemma":[0.00002556149,0.00008441506,0.00005683682,0.0001060594,0.00005703563,0.00007398576,0.00001479043,0.000045886,0.00003963471],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000007068055,"about_ca_system_score_gemma":0.000004253092,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005370312,"about_ca_topic_score_gemma":0.000002612867,"domain_scores_codex":[0.9993537,0.00003738152,0.000215809,0.000140121,0.0001092491,0.0001437039],"domain_scores_gemma":[0.9996046,0.00008143725,0.00003505815,0.0001843338,0.00003536995,0.00005923652],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"bench_or_experimental","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.0005166725,0.0002868248,0.02115696,0.001210344,0.000531861,0.00002177492,0.002666398,0.008045297,0.4937171,0.2428794,0.002983756,0.2259835],"study_design_scores_gemma":[0.004346197,0.0004531269,0.009833884,0.0007451387,0.0001163312,0.0000291742,0.0002695853,0.1368905,0.8058209,0.007420524,0.03295127,0.001123426],"study_design_candidate":"bench_or_experimental","study_design_consensus":"bench_or_experimental","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9923745,0.0005058366,0.004521283,0.00003332061,0.000294442,0.0001336538,0.00003287602,0.0001649368,0.00193915],"genre_scores_gemma":[0.9987171,0.00027052,0.00049187,0.00002567719,0.000162828,0.000006240823,0.000005785727,0.00002746795,0.0002924815],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3121037,"threshold_uncertainty_score":0.3442346,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007260602651030938,"score_gpt":0.2087422465767668,"score_spread":0.2014816439257359,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}