{"id":"https://openalex.org/W4396597221","doi":"https://doi.org/10.1109/tit.2024.3395545","title":"Projective Essential Idempotents","display_name":"Projective Essential Idempotents","publication_year":2024,"publication_date":"2024-05-02","ids":{"openalex":"https://openalex.org/W4396597221","doi":"https://doi.org/10.1109/tit.2024.3395545"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2024.3395545","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2024.3395545","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.1109/TIT.2024.3395545","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022856698","display_name":"A. Duarte","orcid":"https://orcid.org/0000-0001-9449-1231"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andr\u00e9 Duarte","raw_affiliation_strings":["Mathematics and Computing Sciences Institute (ICMC), University of S&#x00E3;o Paulo (USP), S&#x00E3;o Paulo, Brazil"],"raw_orcid":"https://orcid.org/0000-0001-9449-1231","affiliations":[{"raw_affiliation_string":"Mathematics and Computing Sciences Institute (ICMC), University of S&#x00E3;o Paulo (USP), S&#x00E3;o Paulo, Brazil","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5022856698"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5557,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.69404458,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"70","issue":"8","first_page":"5566","last_page":"5572"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.998199999332428,"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":0.998199999332428,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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":0.9962999820709229,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/projective-test","display_name":"Projective test","score":0.6300160884857178},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5218918919563293},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.46013468503952026},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38531821966171265},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3522416353225708},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3430887460708618}],"concepts":[{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.6300160884857178},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5218918919563293},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.46013468503952026},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38531821966171265},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3522416353225708},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3430887460708618}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2024.3395545","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2024.3395545","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:003215221","is_oa":true,"landing_page_url":"https://doi.org/10.1109/TIT.2024.3395545","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"instacron:USP","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:003215221","is_oa":true,"landing_page_url":"https://doi.org/10.1109/TIT.2024.3395545","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"instacron:USP","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1508421660","https://openalex.org/W1569612250","https://openalex.org/W2032621156","https://openalex.org/W2056903967","https://openalex.org/W2153936403","https://openalex.org/W2317746472","https://openalex.org/W2551970957","https://openalex.org/W2576983704","https://openalex.org/W3169477034","https://openalex.org/W4234162184","https://openalex.org/W4250680851","https://openalex.org/W4309757106","https://openalex.org/W4311227523","https://openalex.org/W4365505970"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2001489718","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2024319036","https://openalex.org/W2142036596","https://openalex.org/W1549557214"],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"the":[3,26,31],"concept":[4],"of":[5,28,48],"projective":[6,56,67],"essential":[7,57,68],"idempotents.":[8,69],"These":[9],"are":[10],"primitive":[11],"central":[12],"idempotents":[13],"in":[14],"a":[15,49,55,63],"twisted":[16,50],"group":[17,51],"algebra.":[18],"The":[19],"first":[20],"main":[21,33],"result":[22],"provides":[23],"conditions":[24],"for":[25],"existence":[27],"them.":[29],"In":[30],"second":[32],"result,":[34],"we":[35],"prove":[36],"that":[37],"every":[38],"q-ary":[39],"simplex":[40],"code":[41],"can":[42],"be":[43],"seen":[44],"as":[45],"an":[46],"ideal":[47],"algebra":[52],"generated":[53],"by":[54,61],"idempotent.":[58],"We":[59],"conclude":[60],"describing":[62],"decoding":[64],"process":[65],"using":[66]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2025-12-22T23:10:17.713674","created_date":"2025-10-10T00:00:00"}
