{"id":"W2070033202","doi":"10.1016/j.ffa.2014.12.003","title":"A probabilistic approach to value sets of polynomials over finite fields","year":2015,"lang":"en","type":"article","venue":"Finite Fields and Their Applications","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"Carleton University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Finite field; Coset; Polynomial; Discrete mathematics; Distribution (mathematics); Combinatorics; Random variable; Infinity; Expected value; Value (mathematics); Random field; Finite set; Order (exchange); Statistics; 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":[0.0003178016,0.0001249112,0.0001756945,0.0001125558,0.00009341517,0.00006226247,0.0004891242,0.0001019756,0.000007217818],"category_scores_gemma":[0.00006895393,0.0001026459,0.0000673007,0.0004808264,0.00005074972,0.00009679569,0.0002174493,0.0001187724,0.00000998347],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000006228103,"about_ca_system_score_gemma":0.00004574045,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002872695,"about_ca_topic_score_gemma":0.000004548159,"domain_scores_codex":[0.9991652,0.00005279088,0.00021403,0.0003045842,0.00009669882,0.0001666319],"domain_scores_gemma":[0.9986914,0.0003925848,0.00007062518,0.0006180308,0.00007127324,0.0001561143],"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":[0.00001760927,0.0002030398,0.0001476943,0.00004033008,0.00002899518,2.335656e-7,0.004320553,0.001529063,0.00005490523,0.9712572,0.001286011,0.02111441],"study_design_scores_gemma":[0.0006944914,0.0004492628,0.001227307,0.00004931292,0.0000289746,0.00001022822,0.0002917547,0.06512024,0.0007276367,0.8722389,0.05863139,0.0005304479],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01234325,0.000121292,0.9711136,0.0006297334,0.00005749625,0.0004443281,0.00003318731,0.00007362466,0.01518351],"genre_scores_gemma":[0.9862151,0.000007572084,0.01272868,0.000632229,0.00005319351,0.0002544363,0.000008729155,0.000006265925,0.00009379377],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9738718,"threshold_uncertainty_score":0.4185778,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03058453526743701,"score_gpt":0.252485138880437,"score_spread":0.221900603613,"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."}}