{"id":"https://openalex.org/W2045136060","doi":"https://doi.org/10.1109/tit.2012.2210386","title":"The Weight Distributions of Cyclic Codes and Elliptic Curves","display_name":"The Weight Distributions of Cyclic Codes and Elliptic Curves","publication_year":2012,"publication_date":"2012-08-06","ids":{"openalex":"https://openalex.org/W2045136060","doi":"https://doi.org/10.1109/tit.2012.2210386","mag":"2045136060"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2012.2210386","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2210386","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/A5115591423","display_name":"Baocheng Wang","orcid":"https://orcid.org/0009-0008-4627-592X"},"institutions":[{"id":"https://openalex.org/I1456306","display_name":"North China University of Technology","ror":"https://ror.org/01nky7652","country_code":"CN","type":"education","lineage":["https://openalex.org/I1456306"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Baocheng Wang","raw_affiliation_strings":["College of Information Engineering, North-China University of Technology, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Information Engineering, North-China University of Technology, Beijing, China","institution_ids":["https://openalex.org/I1456306"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054829854","display_name":"Chunming Tang","orcid":"https://orcid.org/0000-0001-9599-851X"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chunming Tang","raw_affiliation_strings":["Laboratory of Mathematics and Applied Mathematics, Chinese Ministry of Education, and the School of Mathematical Sciences, Peking University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Mathematics and Applied Mathematics, Chinese Ministry of Education, and the School of Mathematical Sciences, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018708611","display_name":"Yanfeng Qi","orcid":"https://orcid.org/0000-0003-1381-5471"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanfeng Qi","raw_affiliation_strings":["Laboratory of Mathematics and Applied Mathematics, Chinese Ministry of Education, and the School of Mathematical Sciences, Peking University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Mathematics and Applied Mathematics, Chinese Ministry of Education, and the School of Mathematical Sciences, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071134614","display_name":"Yixian Yang","orcid":"https://orcid.org/0000-0001-8067-4774"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yixian Yang","raw_affiliation_strings":["Information Security Center, Beijing University of Posts and Telecommunications, Beijing, China","Research Center on Fictitious Economy and Data Science, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information Security Center, Beijing University of Posts and Telecommunications, Beijing, China","institution_ids":["https://openalex.org/I139759216"]},{"raw_affiliation_string":"Research Center on Fictitious Economy and Data Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100956729","display_name":"Maozhi Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Maozhi Xu","raw_affiliation_strings":["Laboratory of Mathematics and Applied Mathematics, Chinese Ministry of Education, and the School of Mathematical Sciences, Peking University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Mathematics and Applied Mathematics, Chinese Ministry of Education, and the School of Mathematical Sciences, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":22.5565,"has_fulltext":false,"cited_by_count":64,"citation_normalized_percentile":{"value":0.99543482,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"58","issue":"12","first_page":"7253","last_page":"7259"},"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9779000282287598,"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/T13779","display_name":"Cancer Mechanisms and Therapy","score":0.9488999843597412,"subfield":{"id":"https://openalex.org/subfields/2734","display_name":"Pathology and Forensic Medicine"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.6087108254432678},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5385367274284363},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.533029317855835},{"id":"https://openalex.org/keywords/weight-distribution","display_name":"Weight distribution","score":0.5237762331962585},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4799385666847229},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4786606729030609},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4368242621421814},{"id":"https://openalex.org/keywords/cyclic-code","display_name":"Cyclic code","score":0.4359036386013031},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.39118561148643494},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2755407691001892},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.25301384925842285},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22561252117156982},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14482536911964417},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.1296992003917694},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07520616054534912}],"concepts":[{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.6087108254432678},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5385367274284363},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.533029317855835},{"id":"https://openalex.org/C25432639","wikidata":"https://www.wikidata.org/wiki/Q3711790","display_name":"Weight distribution","level":2,"score":0.5237762331962585},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4799385666847229},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4786606729030609},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4368242621421814},{"id":"https://openalex.org/C2096984","wikidata":"https://www.wikidata.org/wiki/Q245464","display_name":"Cyclic code","level":5,"score":0.4359036386013031},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.39118561148643494},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2755407691001892},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.25301384925842285},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22561252117156982},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14482536911964417},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.1296992003917694},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07520616054534912},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2012.2210386","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2210386","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:oai:CiteSeerX.psu:10.1.1.765.1333","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.765.1333","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1109.0628.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W234588615","https://openalex.org/W1486898453","https://openalex.org/W1534925464","https://openalex.org/W1556443961","https://openalex.org/W1569014707","https://openalex.org/W1587687098","https://openalex.org/W1988094325","https://openalex.org/W2014296474","https://openalex.org/W2015850851","https://openalex.org/W2020484625","https://openalex.org/W2030255923","https://openalex.org/W2033038403","https://openalex.org/W2034011421","https://openalex.org/W2040588796","https://openalex.org/W2076272501","https://openalex.org/W2089606264","https://openalex.org/W2099197486","https://openalex.org/W2105271809","https://openalex.org/W2147067885","https://openalex.org/W2171498600","https://openalex.org/W2607694892","https://openalex.org/W3004074467","https://openalex.org/W4205498948","https://openalex.org/W6773698663"],"related_works":["https://openalex.org/W2368816803","https://openalex.org/W2321561475","https://openalex.org/W2261254933","https://openalex.org/W2238578788","https://openalex.org/W2533621910","https://openalex.org/W4248511311","https://openalex.org/W2157984728","https://openalex.org/W2963553930","https://openalex.org/W2963630585","https://openalex.org/W1793009983"],"abstract_inverted_index":{"Cyclic":[0],"codes":[1,8,18,37,48,67,74],"with":[2,75],"two":[3,76],"zeros":[4,77],"and":[5,12,25],"their":[6],"dual":[7,66],"as":[9],"a":[10,54,79],"practically":[11],"theoretically":[13],"interesting":[14],"class":[15,55],"of":[16,31,35,46,56,65,68],"linear":[17],"have":[19],"been":[20],"studied":[21],"for":[22,78],"many":[23,27],"years":[24],"find":[26],"applications.":[28],"The":[29],"determination":[30],"the":[32,43,62],"weight":[33,44,63],"distributions":[34,45,64],"such":[36],"is":[38,87],"an":[39,88],"open":[40],"problem.":[41],"Generally,":[42],"cyclic":[47,73],"are":[49],"difficult":[50],"to":[51],"determine.":[52],"Utilizing":[53],"elliptic":[57],"curves,":[58],"this":[59],"paper":[60],"determines":[61],"<i":[69,84],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[70,85],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">q</i>":[71,86],"-ary":[72],"few":[80],"more":[81],"cases,":[82],"where":[83],"odd":[89],"prime":[90],"power.":[91]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":20},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":15},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}