{"id":"W2963525585","doi":"10.1016/j.disc.2018.10.021","title":"Balancedly splittable Hadamard matrices","year":2018,"lang":"en","type":"article","venue":"Discrete Mathematics","topic":"graph theory and CDMA systems","field":"Engineering","cited_by":8,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Lethbridge","funders":"Natural Sciences and Engineering Research Council of Canada; Japan Society for the Promotion of Science; Soochow University","keywords":"Mathematics; Hadamard transform; Complex Hadamard matrix; Hadamard product; Combinatorics; Association scheme; Hadamard matrix; Hadamard's inequality; Diagonalizable matrix; Hadamard three-lines theorem; Connection (principal bundle); Discrete mathematics; Eigenvalues and eigenvectors; Symmetric matrix; Geometry; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0001929739,0.0001531919,0.0002033851,0.00005527951,0.00007796019,0.00006377235,0.0002036674,0.0000638263,0.0002331316],"category_scores_gemma":[0.00001702919,0.0001298989,0.00006571943,0.0001945118,0.00006326123,0.0001150506,0.00002558703,0.00007496161,0.0007303379],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001647149,"about_ca_system_score_gemma":0.000004613261,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002321859,"about_ca_topic_score_gemma":0.000003247071,"domain_scores_codex":[0.9992206,0.00001294116,0.0002412086,0.0001128797,0.0001484214,0.0002639119],"domain_scores_gemma":[0.9994739,0.00004332737,0.00003812012,0.0003460484,0.00003193264,0.000066696],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00003795022,0.0001866509,0.002181749,0.005279023,0.0006609442,0.00004283182,0.01831325,0.001424071,0.03242704,0.8673456,0.06728515,0.004815698],"study_design_scores_gemma":[0.001761983,0.0004049078,0.001151019,0.001385559,0.0002939974,0.0001903354,0.007414642,0.3256403,0.07663989,0.3650869,0.2171006,0.00292986],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5606173,0.0007366225,0.04958087,0.00004002554,0.001141656,0.0003491986,0.00003665239,0.001105214,0.3863925],"genre_scores_gemma":[0.993149,0.00002266283,0.005410645,0.00002165487,0.0002419907,0.00001880847,0.000005189844,0.00004333137,0.001086761],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5022587,"threshold_uncertainty_score":0.9387259,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007210121603247261,"score_gpt":0.2110867398563951,"score_spread":0.2038766182531479,"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."}}