{"id":"https://openalex.org/W4407764381","doi":"https://doi.org/10.48550/arxiv.2502.13531","title":"Quotients of skew polynomial rings: new constructions of division algebras and MRD codes","display_name":"Quotients of skew polynomial rings: new constructions of division algebras and MRD codes","publication_year":2025,"publication_date":"2025-02-19","ids":{"openalex":"https://openalex.org/W4407764381","doi":"https://doi.org/10.48550/arxiv.2502.13531"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2502.13531","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2502.13531","pdf_url":"https://arxiv.org/pdf/2502.13531","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2502.13531","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084563220","display_name":"F. J. Lobillo","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lobillo, F. J.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101964663","display_name":"Paolo Santonastaso","orcid":"https://orcid.org/0000-0002-9525-7049"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Santonastaso, Paolo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5038859418","display_name":"John Sheekey","orcid":"https://orcid.org/0000-0002-8590-0301"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sheekey, John","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5084563220"],"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":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9811999797821045,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/skew","display_name":"Skew","score":0.7832949161529541},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.686530351638794},{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.6538825035095215},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.6526968479156494},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.6195769309997559},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4188104271888733},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.41524964570999146},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3846125900745392},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3529234230518341},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33789512515068054},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20916002988815308},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.15912076830863953}],"concepts":[{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.7832949161529541},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.686530351638794},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.6538825035095215},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.6526968479156494},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.6195769309997559},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4188104271888733},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.41524964570999146},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3846125900745392},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3529234230518341},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33789512515068054},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20916002988815308},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.15912076830863953},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2502.13531","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2502.13531","pdf_url":"https://arxiv.org/pdf/2502.13531","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2502.13531","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2502.13531","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2502.13531","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2502.13531","pdf_url":"https://arxiv.org/pdf/2502.13531","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4290802965","https://openalex.org/W97789383","https://openalex.org/W2105011602","https://openalex.org/W3213353046","https://openalex.org/W2296020509","https://openalex.org/W4394825304","https://openalex.org/W3147951423","https://openalex.org/W4287663006","https://openalex.org/W2606484672","https://openalex.org/W4299612196"],"abstract_inverted_index":{"We":[0],"achieve":[1],"new":[2,47,70,92],"results":[3],"on":[4],"skew":[5,18,29],"polynomial":[6,19,30],"rings":[7],"and":[8,53,62,94,106],"their":[9],"quotients,":[10],"including":[11],"the":[12,22,25,32,44,110],"first":[13],"explicit":[14],"example":[15],"of":[16,24,27,34,46,101,109],"a":[17,28,78],"ring":[20],"where":[21],"ratio":[23],"degree":[26,33,83],"to":[31,43],"its":[35],"bound":[36],"is":[37,77],"not":[38],"extremal.":[39],"These":[40,103],"methods":[41],"lead":[42],"construction":[45],"(not":[48],"necessarily":[49],"associative)":[50],"division":[51,64,72],"algebras":[52,73],"maximum":[54],"rank":[55],"distance":[56],"(MRD)":[57],"codes":[58,96],"over":[59],"both":[60],"finite":[61,88],"infinite":[63],"rings.":[65],"In":[66],"particular,":[67],"we":[68,90],"construct":[69],"non-associative":[71],"whose":[74],"right":[75],"nucleus":[76],"central":[79],"simple":[80],"algebra":[81],"having":[82],"greater":[84],"than":[85],"1.":[86],"Over":[87],"fields,":[89],"obtain":[91],"semifields":[93],"MRD":[95],"for":[97],"infinitely":[98],"many":[99,108],"choices":[100],"parameters.":[102],"families":[104],"extend":[105],"contain":[107],"best":[111],"previously":[112],"known":[113],"constructions.":[114]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}
