{"id":"https://openalex.org/W4402570893","doi":"https://doi.org/10.1109/tit.2024.3462712","title":"Generator Polynomials of Cyclic Expurgated or Extended Goppa Codes","display_name":"Generator Polynomials of Cyclic Expurgated or Extended Goppa Codes","publication_year":2024,"publication_date":"2024-09-17","ids":{"openalex":"https://openalex.org/W4402570893","doi":"https://doi.org/10.1109/tit.2024.3462712"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2024.3462712","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2024.3462712","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070478712","display_name":"Xue Jia","orcid":"https://orcid.org/0000-0003-1945-6705"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xue Jia","raw_affiliation_strings":["School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0003-1945-6705","affiliations":[{"raw_affiliation_string":"School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102000741","display_name":"Fengwei Li","orcid":"https://orcid.org/0000-0002-9493-2890"},"institutions":[{"id":"https://openalex.org/I41198531","display_name":"Nanjing University of Posts and Telecommunications","ror":"https://ror.org/043bpky34","country_code":"CN","type":"education","lineage":["https://openalex.org/I41198531"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fengwei Li","raw_affiliation_strings":["College of Science, Nanjing University of Posts and Telecommunications, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-9493-2890","affiliations":[{"raw_affiliation_string":"College of Science, Nanjing University of Posts and Telecommunications, Nanjing, China","institution_ids":["https://openalex.org/I41198531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066569293","display_name":"Huan Sun","orcid":"https://orcid.org/0000-0002-2252-2227"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huan Sun","raw_affiliation_strings":["School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-2252-2227","affiliations":[{"raw_affiliation_string":"School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100786671","display_name":"Qin Yue","orcid":"https://orcid.org/0000-0002-2873-5549"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qin Yue","raw_affiliation_strings":["School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-2873-5549","affiliations":[{"raw_affiliation_string":"School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5070478712"],"corresponding_institution_ids":["https://openalex.org/I9842412"],"apc_list":null,"apc_paid":null,"fwci":0.3311,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.65734381,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"70","issue":"11","first_page":"7711","last_page":"7722"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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":0.9998000264167786,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9839000105857849,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9725000262260437,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/mathematics","display_name":"Mathematics","score":0.47693270444869995},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.43971773982048035},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.4184388518333435},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3913816511631012},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35562431812286377},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.3435611128807068},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32356148958206177},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25434526801109314},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2293585240840912},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.12754476070404053},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.12518572807312012},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11232736706733704}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47693270444869995},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.43971773982048035},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.4184388518333435},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3913816511631012},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35562431812286377},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.3435611128807068},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32356148958206177},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25434526801109314},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2293585240840912},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.12754476070404053},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.12518572807312012},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11232736706733704},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2024.3462712","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2024.3462712","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4665115554","display_name":null,"funder_award_id":"12171420","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6597487595","display_name":null,"funder_award_id":"ZR2021MA046","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G6852048583","display_name":null,"funder_award_id":"BK20200268","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G7338538566","display_name":null,"funder_award_id":"2021ZD0302902","funder_id":"https://openalex.org/F4320313655","funder_display_name":"Foundation for Research, Science and Technology"},{"id":"https://openalex.org/G8021785736","display_name":null,"funder_award_id":"62172219","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320313655","display_name":"Foundation for Research, Science and Technology","ror":null},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W115335709","https://openalex.org/W1488034582","https://openalex.org/W1606480398","https://openalex.org/W1978755349","https://openalex.org/W1990361074","https://openalex.org/W2005583345","https://openalex.org/W2046801204","https://openalex.org/W2063444680","https://openalex.org/W2064329148","https://openalex.org/W2078870121","https://openalex.org/W2104464473","https://openalex.org/W2110783808","https://openalex.org/W2152240370","https://openalex.org/W2156837852","https://openalex.org/W2170304442","https://openalex.org/W2895239415","https://openalex.org/W3000951904","https://openalex.org/W4206775542","https://openalex.org/W4221147780","https://openalex.org/W4249367262","https://openalex.org/W4282572216","https://openalex.org/W4285112024","https://openalex.org/W4294698941","https://openalex.org/W4296558673","https://openalex.org/W4386976624","https://openalex.org/W4389104608","https://openalex.org/W6770380337"],"related_works":["https://openalex.org/W135568846","https://openalex.org/W2460434904","https://openalex.org/W1789159349","https://openalex.org/W2113911300","https://openalex.org/W2151857680","https://openalex.org/W832867880","https://openalex.org/W2147254059","https://openalex.org/W4386066307","https://openalex.org/W917159298","https://openalex.org/W1975697476"],"abstract_inverted_index":{"Classical":[0],"Goppa":[1,30,82],"codes":[2,8,31,83],"are":[3,15,24],"a":[4,16,33,38,51,65],"well-known":[5],"class":[6],"of":[7,19,77],"with":[9,32,37,54],"applications":[10],"in":[11],"code-based":[12],"cryptography,":[13],"which":[14],"special":[17],"case":[18],"alternant":[20],"codes.":[21],"Many":[22],"papers":[23],"devoted":[25],"to":[26,109],"the":[27,74,90],"search":[28],"for":[29],"cyclic":[34,39,78],"extension":[35],"or":[36,80],"parity-check":[40],"subcode.":[41],"Let":[42],"<inline-formula":[43,55,95],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[44,56,96],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[45,57,97],"<tex-math":[46,58,98],"notation=\"LaTeX\">$\\Bbb":[47],"F_{q}$":[48],"</tex-math></inline-formula>":[49,60],"be":[50],"finite":[52],"field":[53],"notation=\"LaTeX\">$q=2^{l}$":[59],"elements,":[61],"where":[62],"l":[63],"is":[64],"positive":[66],"integer.":[67],"In":[68],"this":[69],"paper,":[70],"we":[71,105],"determine":[72],"all":[73],"generator":[75],"polynomials":[76],"expurgated":[79],"extended":[81],"under":[84],"some":[85,107],"prescribed":[86],"permutations":[87],"induced":[88],"by":[89],"projective":[91],"general":[92],"linear":[93],"automorphism":[94],"notation=\"LaTeX\">$A":[99],"\\in":[100],"PGL_{2}(\\Bbb":[101],"F_{q})$":[102],"</tex-math></inline-formula>.":[103],"Moreover,":[104],"provide":[106],"examples":[108],"support":[110],"our":[111],"findings.":[112]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-12-21T23:12:01.093139","created_date":"2025-10-10T00:00:00"}