{"id":"https://openalex.org/W2004202980","doi":"https://doi.org/10.1007/s10623-010-9424-6","title":"An alternative class of irreducible polynomials for optimal extension fields","display_name":"An alternative class of irreducible polynomials for optimal extension fields","publication_year":2010,"publication_date":"2010-08-11","ids":{"openalex":"https://openalex.org/W2004202980","doi":"https://doi.org/10.1007/s10623-010-9424-6","mag":"2004202980"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-010-9424-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-010-9424-6","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100451133","display_name":"Yin Li","orcid":"https://orcid.org/0000-0002-9529-8481"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yin Li","raw_affiliation_strings":["School of Information Security Engineering, Shanghai Jiaotong University, Shanghai, China","School of Information Security Engineering, Shanghai Jiaotong University, Shanghai, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Security Engineering, Shanghai Jiaotong University, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"School of Information Security Engineering, Shanghai Jiaotong University, Shanghai, China#TAB#","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087546979","display_name":"Gongliang Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gong-liang Chen","raw_affiliation_strings":["School of Information Security Engineering, Shanghai Jiaotong University, Shanghai, China","School of Information Security Engineering, Shanghai Jiaotong University, Shanghai, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Security Engineering, Shanghai Jiaotong University, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"School of Information Security Engineering, Shanghai Jiaotong University, Shanghai, China#TAB#","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100391361","display_name":"Jianhua Li","orcid":"https://orcid.org/0000-0002-6831-3973"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian-hua Li","raw_affiliation_strings":["Department of Electronic Engineering, Shanghai Jiaotong University, Shanghai, China","Department of Electronic Engineering,Shanghai Jiaotong University, shanghai, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Shanghai Jiaotong University, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"Department of Electronic Engineering,Shanghai Jiaotong University, shanghai, China#TAB#","institution_ids":["https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100451133"],"corresponding_institution_ids":["https://openalex.org/I183067930"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13462324,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"60","issue":"2","first_page":"171","last_page":"182"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998000264167786,"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/T11130","display_name":"Coding theory and cryptography","score":0.9976000189781189,"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/T10237","display_name":"Cryptography and Data Security","score":0.9876999855041504,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/trinomial","display_name":"Trinomial","score":0.9313855171203613},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.7395429611206055},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6539342999458313},{"id":"https://openalex.org/keywords/irreducible-polynomial","display_name":"Irreducible polynomial","score":0.6407240629196167},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.6239062547683716},{"id":"https://openalex.org/keywords/cryptosystem","display_name":"Cryptosystem","score":0.5922641158103943},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.49569880962371826},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4496689736843109},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4456091821193695},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4408690929412842},{"id":"https://openalex.org/keywords/irreducible-element","display_name":"Irreducible element","score":0.4161715805530548},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4137408435344696},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38446927070617676},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.343095600605011},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30908870697021484},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2715049684047699},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.22019729018211365},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.21580713987350464},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15593209862709045},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.06822225451469421},{"id":"https://openalex.org/keywords/fundamental-representation","display_name":"Fundamental representation","score":0.06374126672744751}],"concepts":[{"id":"https://openalex.org/C6791720","wikidata":"https://www.wikidata.org/wiki/Q1670509","display_name":"Trinomial","level":2,"score":0.9313855171203613},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.7395429611206055},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6539342999458313},{"id":"https://openalex.org/C165030954","wikidata":"https://www.wikidata.org/wiki/Q1476663","display_name":"Irreducible polynomial","level":4,"score":0.6407240629196167},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6239062547683716},{"id":"https://openalex.org/C6295992","wikidata":"https://www.wikidata.org/wiki/Q976521","display_name":"Cryptosystem","level":3,"score":0.5922641158103943},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.49569880962371826},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4496689736843109},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4456091821193695},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4408690929412842},{"id":"https://openalex.org/C15376144","wikidata":"https://www.wikidata.org/wiki/Q2989575","display_name":"Irreducible element","level":5,"score":0.4161715805530548},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4137408435344696},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38446927070617676},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.343095600605011},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30908870697021484},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2715049684047699},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.22019729018211365},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.21580713987350464},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15593209862709045},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.06822225451469421},{"id":"https://openalex.org/C5106717","wikidata":"https://www.wikidata.org/wiki/Q3427416","display_name":"Fundamental representation","level":4,"score":0.06374126672744751},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C183877218","wikidata":"https://www.wikidata.org/wiki/Q7979858","display_name":"Weight","level":3,"score":0.0},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10623-010-9424-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-010-9424-6","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320337392","display_name":"Division of Electrical, Communications and Cyber Systems","ror":"https://ror.org/01krpsy48"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W202363749","https://openalex.org/W1471103927","https://openalex.org/W1501115028","https://openalex.org/W1562183207","https://openalex.org/W1566347616","https://openalex.org/W1569612250","https://openalex.org/W1586812950","https://openalex.org/W1595724787","https://openalex.org/W2036378739","https://openalex.org/W2056164327","https://openalex.org/W2056748176","https://openalex.org/W2085259382","https://openalex.org/W2110692871","https://openalex.org/W2613956024","https://openalex.org/W2752853835","https://openalex.org/W2952470461","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2122699041","https://openalex.org/W901371731","https://openalex.org/W2039888964","https://openalex.org/W2133814675","https://openalex.org/W2145897696","https://openalex.org/W3139299461","https://openalex.org/W1976396586","https://openalex.org/W1969425915","https://openalex.org/W1995503477","https://openalex.org/W2217178611"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}