{"id":"W2074881723","doi":"10.1016/j.jcta.2010.11.005","title":"Relatively prime polynomials and nonsingular Hankel matrices over finite fields","year":2010,"lang":"en","type":"article","venue":"Journal of Combinatorial Theory Series A","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":21,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Invertible matrix; Hankel matrix; Coprime integers; Monic polynomial; Finite field; Rank (graph theory); Prime (order theory); Combinatorics; Pure mathematics; Discrete mathematics; Algebra over a field; Polynomial; Mathematical analysis","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":[0.001921384,0.0001634136,0.0003121752,0.0002212433,0.0002151857,0.0002784321,0.0006413166,0.0001515876,0.00006441347],"category_scores_gemma":[0.0005054005,0.0001347153,0.0001583831,0.0003063614,0.0001935138,0.001190227,0.0002066876,0.0005549216,0.000002704029],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000009545762,"about_ca_system_score_gemma":0.00009770752,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000219754,"about_ca_topic_score_gemma":9.62195e-7,"domain_scores_codex":[0.9986844,0.0002601473,0.0004153475,0.000166657,0.0002695042,0.0002039632],"domain_scores_gemma":[0.9980402,0.000856622,0.0004759365,0.0003135216,0.0001753832,0.0001383324],"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":[0.0003974814,0.00005920855,0.0002861758,0.000007000476,0.0000617462,0.00003246331,0.001062078,0.000002034426,0.004447561,0.9888992,0.0001786853,0.00456639],"study_design_scores_gemma":[0.0009187764,0.000625517,0.001032532,0.00004075397,0.00003137665,0.000162073,0.00005663056,0.0000383128,0.006300431,0.9738013,0.0168083,0.0001840213],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.94072,0.0006584213,0.04373117,0.0008334572,0.01135696,0.0001296222,0.000002693825,0.00006360325,0.00250413],"genre_scores_gemma":[0.9929914,0.00006002029,0.006087083,0.0001222358,0.0006138793,0.000001018492,1.444063e-7,0.000009911286,0.0001143416],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05227143,"threshold_uncertainty_score":0.549353,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.005469718997047604,"score_gpt":0.222361286126096,"score_spread":0.2168915671290484,"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."}}