{"id":"W2744871629","doi":"10.1007/s10623-017-0452-3","title":"New constructions of permutation polynomials of the form $$x^rh\\left( x^{q-1}\\right) $$ x r h x q - 1 over $${\\mathbb F}_{q^2}$$ F q 2","year":2017,"lang":"en","type":"article","venue":"Designs Codes and Cryptography","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":39,"is_retracted":false,"has_abstract":false,"ca_institutions":"Carleton University","funders":"National Key Research and Development Program of China; Program for New Century Excellent Talents in University; State Key Laboratory of Cryptography","keywords":"Trinomial; Permutation (music); Multiplicative function; Cyclic permutation; Permutation graph; Finite field; Partial permutation; Generalized permutation 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":[0.0003679633,0.0001962234,0.0003135652,0.0002521584,0.0007311159,0.0002207285,0.001165751,0.00009831254,0.00006171289],"category_scores_gemma":[0.00004349392,0.0001438191,0.0003534046,0.0003273023,0.0006011344,0.000566416,0.0002513955,0.0001224581,9.784874e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000005999409,"about_ca_system_score_gemma":0.0000891094,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001229143,"about_ca_topic_score_gemma":0.00003998981,"domain_scores_codex":[0.9986837,0.00009437839,0.0003851645,0.0003208382,0.0002743661,0.000241572],"domain_scores_gemma":[0.9979881,0.0001458475,0.0005321187,0.001112635,0.0001099984,0.0001112753],"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":[0.00003315802,0.00005388296,0.02238381,0.00004225664,0.0001122347,0.000001160049,0.001197507,0.000005974136,0.01665307,0.9354339,0.0007693161,0.02331371],"study_design_scores_gemma":[0.001539738,0.0003508674,0.2469363,0.0002362941,0.0001717461,0.00007024885,0.0002928054,0.0009615742,0.06461336,0.6807802,0.003491429,0.0005553958],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.519299,0.0003861006,0.4744396,0.0004259022,0.0005651183,0.0003684941,0.00003621454,0.00007565685,0.004403853],"genre_scores_gemma":[0.9749569,0.00008956735,0.02480074,0.0000619555,0.00004693932,0.000006128568,0.000001267866,0.000009646439,0.00002687253],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4556578,"threshold_uncertainty_score":0.5864773,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01736009532675113,"score_gpt":0.2515466679506085,"score_spread":0.2341865726238574,"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."}}