{"id":"W3158772284","doi":"10.48550/arxiv.2105.02374","title":"The additive index of polynomials over finite fields","year":2021,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Finite field; Multiplicative function; Mathematics; Permutation (music); Character (mathematics); Polynomial; Set (abstract data type); Index (typography); Field (mathematics); Combinatorics; Pure mathematics; Discrete mathematics; Algebra over a field; Mathematical analysis; Computer science; Physics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001822483,0.0006699028,0.0008110474,0.00275458,0.001257792,0.004548302,0.001328117,0.0007529663,0.003172983],"category_scores_gemma":[0.007912579,0.00032596,0.0006046523,0.002194984,0.004179526,0.01117569,0.002505671,0.003392476,0.0007062689],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001367351,"about_ca_system_score_gemma":0.0006672814,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000202205,"about_ca_topic_score_gemma":0.0001552886,"domain_scores_codex":[0.9975002,0.0004352347,0.0001499877,0.0004529743,0.001119413,0.000342166],"domain_scores_gemma":[0.994661,0.002976794,0.0006213817,0.0007370269,0.0005592318,0.0004445093],"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":[0.00002351463,0.00001477729,0.0002391343,0.00002900016,0.000004090842,0.00004618699,0.0001008768,0.0008390194,0.00116316,0.992192,0.0002419358,0.005106323],"study_design_scores_gemma":[0.000007737664,0.00005174893,0.0003113232,0.00003053402,0.00001307651,0.0002481212,0.00007388589,0.008577048,0.002625678,0.9819258,0.006113281,0.00002166705],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.372537,0.003754627,0.5100541,0.003067551,0.0009078165,0.00007240465,0.0004325861,0.0004075044,0.1087663],"genre_scores_gemma":[0.9426209,0.001487508,0.04553636,0.0003461805,0.001206638,0.00006024344,0.0001927935,0.0001032031,0.008446085],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004548302,"threshold_uncertainty_score":0.01061469,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03920610609754951,"score_gpt":0.1795727729320646,"score_spread":0.140366666834515,"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."}}