{"id":"https://openalex.org/W7225629374","doi":"https://doi.org/10.5281/zenodo.24054196","title":"Projective Quotient Polynomials and Kernel-Weight Layers over Finite Fields Calculations related to Question 2 of Beierle","display_name":"Projective Quotient Polynomials and Kernel-Weight Layers over Finite Fields Calculations related to Question 2 of Beierle","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225629374","doi":"https://doi.org/10.5281/zenodo.24054196"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24054196","doi":"https://doi.org/10.5281/zenodo.24054196","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24054196","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24054196","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5161134707","display_name":"Chea Luke Berg","orcid":"https://orcid.org/0009-0001-5957-0898","observed_orcids":["https://orcid.org/0009-0001-5957-0898"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Berg, Chea","raw_affiliation_strings":["Independent Researcher"],"raw_orcid":"https://orcid.org/0009-0001-5957-0898","affiliations":[{"raw_affiliation_string":"Independent Researcher","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5161134707"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9785000085830688,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9785000085830688,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.003599999938160181,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.0027000000700354576,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/finite-fields","display_name":"finite fields","score":0.9359999895095825},{"id":"https://openalex.org/keywords/q-polynomials","display_name":"q-polynomials","score":0.7950000166893005},{"id":"https://openalex.org/keywords/kernel-dimension","display_name":"kernel dimension","score":0.7900000214576721},{"id":"https://openalex.org/keywords/differential-spectra","display_name":"differential spectrum","score":0.8349999785423279}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7767000198364258},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.6804999709129333},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6155999898910522},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.527400016784668},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4756999909877777},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.459199994802475},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.42089998722076416},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4203999936580658},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41839998960494995},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4034000039100647},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.40209999680519104},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.38839998841285706},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.3781999945640564},{"id":"https://openalex.org/C2777044963","wikidata":"https://www.wikidata.org/wiki/Q5384707","display_name":"Equivalence class (music)","level":2,"score":0.36469998955726624},{"id":"https://openalex.org/C174072685","wikidata":"https://www.wikidata.org/wiki/Q1667469","display_name":"Prime power","level":3,"score":0.361299991607666},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.3589000105857849},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.29829999804496765},{"id":"https://openalex.org/C90685605","wikidata":"https://www.wikidata.org/wiki/Q764115","display_name":"Projective line","level":4,"score":0.2924000024795532},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.27959999442100525}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24054196","doi":"https://doi.org/10.5281/zenodo.24054196","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24054196","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24054197","doi":"https://doi.org/10.5281/zenodo.24054197","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24054197","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24054196","doi":"https://doi.org/10.5281/zenodo.24054196","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24054196","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2807901133","https://openalex.org/W2018018612","https://openalex.org/W4403463552","https://openalex.org/W4386875079","https://openalex.org/W2022672563","https://openalex.org/W2044254427","https://openalex.org/W2082121337","https://openalex.org/W2046261350","https://openalex.org/W966068511","https://openalex.org/W2068023453"],"abstract_inverted_index":{"Let":[0],"L":[1,30],"and":[2,23,69],"M":[3,33],"be":[4],"q-polynomials":[5],"on":[6],"Fqn":[7],",":[8],"where":[9],"q":[10],"is":[11,84],"an":[12],"arbitrary":[13],"prime":[14],"power.":[15],"We":[16],"study":[17],"therelationship":[18],"between":[19],"their":[20],"quotient-image":[21,67],"sets":[22],"the":[24,27,40,44,64,66],"dimensions":[25],"of":[26,29,43],"kernels":[28],"\u2212":[31,34],"aXand":[32],"aX.":[35],"A":[36],"projective":[37],"product":[38],"records":[39],"integer":[41],"multiplicities":[42],"quotient":[45],"values.Its":[46],"Moore-determinant":[47],"form":[48],"yields":[49],"principal-minor":[50],"coefficients":[51],"with":[52,57],"Frobenius":[53],"recurrences.These":[54],"relations,":[55],"together":[56],"Newton\u2019s":[58],"identities":[59],"in":[60,70],"characteristic":[61],"p,":[62],"determine":[63,72],"coefficientsfrom":[65],"set":[68],"turn":[71],"each":[73],"kernel":[74],"dimension.":[75],"The":[76],"associateddifferential-spectrum":[77],"calculation":[78],"for":[79],"x":[80],"7":[81],"\u2192":[82],"xL(x)":[83],"included.":[85]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}
