{"id":"https://openalex.org/W2963568817","doi":"https://doi.org/10.1109/tit.2014.2329694","title":"The Weight Distributions of Several Classes of Cyclic Codes From APN Monomials","display_name":"The Weight Distributions of Several Classes of Cyclic Codes From APN Monomials","publication_year":2014,"publication_date":"2014-06-19","ids":{"openalex":"https://openalex.org/W2963568817","doi":"https://doi.org/10.1109/tit.2014.2329694","mag":"2963568817"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2014.2329694","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2329694","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://bora.uib.no/bora-xmlui/bitstream/1956/8430/1/weight_distributions.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100341684","display_name":"Chunlei Li","orcid":"https://orcid.org/0000-0002-3792-769X"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":true,"raw_author_name":"Chunlei Li","raw_affiliation_strings":["Department of Informatics, University of Bergen, Bergen, Norway"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100400586","display_name":"Nian Li","orcid":"https://orcid.org/0000-0003-4913-7844"},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Nian Li","raw_affiliation_strings":["Information Security and National Computing Grid Laboratory, Southwest Jiaotong University, Chengdu, China"],"affiliations":[{"raw_affiliation_string":"Information Security and National Computing Grid Laboratory, Southwest Jiaotong University, Chengdu, China","institution_ids":["https://openalex.org/I4800084"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026698531","display_name":"Tor Helleseth","orcid":"https://orcid.org/0000-0003-1290-3541"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Tor Helleseth","raw_affiliation_strings":["Department of Informatics, University of Bergen, Bergen, Norway"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074480584","display_name":"Cunsheng Ding","orcid":"https://orcid.org/0000-0001-9392-9860"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Cunsheng Ding","raw_affiliation_strings":["Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Hong Kong","institution_ids":["https://openalex.org/I200769079"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100341684"],"corresponding_institution_ids":["https://openalex.org/I4432739"],"apc_list":null,"apc_paid":null,"fwci":9.802,"has_fulltext":true,"cited_by_count":49,"citation_normalized_percentile":{"value":0.98149854,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"60","issue":"8","first_page":"4710","last_page":"4721"},"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":0.9916999936103821,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/combinatorics","display_name":"Combinatorics","score":0.5336751341819763},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.47396108508110046},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4399282932281494},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.420342355966568},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3515423536300659},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26479628682136536},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06597515940666199}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5336751341819763},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.47396108508110046},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4399282932281494},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.420342355966568},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3515423536300659},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26479628682136536},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06597515940666199},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2014.2329694","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2329694","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:bora.uib.no:1956/8430","is_oa":true,"landing_page_url":"https://hdl.handle.net/1956/8430","pdf_url":"https://bora.uib.no/bora-xmlui/bitstream/1956/8430/1/weight_distributions.pdf","source":{"id":"https://openalex.org/S4306400085","display_name":"Bergen Open Research Archive (BORA) (University of Bergen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4432739","host_organization_name":"University of Bergen","host_organization_lineage":["https://openalex.org/I4432739"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"8","raw_type":null},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-64025","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-64025","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"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":"Article"}],"best_oa_location":{"id":"pmh:oai:bora.uib.no:1956/8430","is_oa":true,"landing_page_url":"https://hdl.handle.net/1956/8430","pdf_url":"https://bora.uib.no/bora-xmlui/bitstream/1956/8430/1/weight_distributions.pdf","source":{"id":"https://openalex.org/S4306400085","display_name":"Bergen Open Research Archive (BORA) (University of Bergen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4432739","host_organization_name":"University of Bergen","host_organization_lineage":["https://openalex.org/I4432739"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"8","raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4353521228","display_name":null,"funder_award_id":"61201243","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7730069262","display_name":null,"funder_award_id":"61171095","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323299","display_name":"Norges Forskningsr\u00e5d","ror":"https://ror.org/00epmv149"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2963568817.pdf"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W149695902","https://openalex.org/W1563907129","https://openalex.org/W1587687098","https://openalex.org/W1967292957","https://openalex.org/W1967648774","https://openalex.org/W1982338917","https://openalex.org/W1983796541","https://openalex.org/W1986865829","https://openalex.org/W2012525201","https://openalex.org/W2020484625","https://openalex.org/W2021094554","https://openalex.org/W2034011421","https://openalex.org/W2039170351","https://openalex.org/W2048316651","https://openalex.org/W2083108312","https://openalex.org/W2094825109","https://openalex.org/W2099736138","https://openalex.org/W2110003303","https://openalex.org/W2116631176","https://openalex.org/W2123695891","https://openalex.org/W2130499429","https://openalex.org/W2159712509","https://openalex.org/W2160808756","https://openalex.org/W2171498600","https://openalex.org/W2504274129","https://openalex.org/W2613956024","https://openalex.org/W2963011145"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Let":[0],"m":[1,36,59,213],"\u2265":[2],"3":[3,87,232],"be":[4,10],"an":[5,11,186],"odd":[6,12],"integer":[7,93,113],"and":[8,56,90,150,233],"p":[9,85,230],"prime.":[13],"In":[14,226],"this":[15],"paper,":[16],"a":[17,73,91],"number":[18],"of":[19,21,68,77,123,191,202,229,242],"classes":[20],"three-weight":[22],"cyclic":[23,204,244],"codes":[24,205],"C(1,e)":[25],"over":[26,70],"F":[27,78],"<sub":[28,37,41,60,79,131,134,137,156,159,162,207,214,218,222,247],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[29,38,42,61,80,98,132,135,138,142,145,148,157,160,163,167,171,179,208,215,219,223,248],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">p</sub>":[30,81,136,161],",":[31],"which":[32],"have":[33],"parity-check":[34,211],"polynomial":[35,67,212],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[39,216],"(x)m":[40,217,221],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">e</sub>":[43,220],"(x),":[44],"are":[45,183],"presented":[46],"by":[47],"examining":[48],"general":[49],"conditions":[50],"on":[51],"the":[52,65,120,124,188,199,203,227,237,240,243],"parameters":[53],"p,":[54],"m,":[55],"e,":[57],"where":[58,174],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">i</sub>":[62],"(x)":[63],"is":[64,195],"minimal":[66],"\u03c0-i":[69],"Fp":[71],"for":[72,84,110],"primitive":[74],"element":[75],"\u03c0":[76],"m.":[82],"Furthermore,":[83],"\u2261":[86,104],"(mod":[88,106],"4)":[89],"positive":[92,112],"e":[94,103,235],"satisfying":[95,236],"(p":[96,177],"<sup":[97,141,144,147,166,170,178],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k</sup>":[99],"+":[100],"1)":[101,109],"\u00b7":[102],"2":[105],"pm":[107],"-":[108,181],"some":[111],"k":[114],"with":[115,210],"gcd(m,":[116],"k)":[117],"=":[118,129,154,176,231],"1,":[119],"value":[121,189],"distributions":[122],"exponential":[125],"sums":[126],"T(a,":[127],"b)":[128],"\u03a3x\u2208":[130,155],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">F</sub>":[133,158],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">m</sub>":[139,164],"\u03c9":[140],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Tr(ax+bx</sup>":[143],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">e</sup>":[146,168],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">)</sup>":[149],"S(a,":[151,192],"b,":[152,193],"c)":[153,194],"\u03c9Tr(ax+bx":[165],"+cx":[169],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">s</sup>":[172],"),":[173],"s":[175],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">m</sup>":[180],"1)/2,":[182],"determined.":[184],"As":[185],"application,":[187],"distribution":[190,201],"utilized":[196],"to":[197],"derive":[198],"weight":[200],"C":[206,246],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">(1,e,s)</sub>":[209,249],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">s</sub>":[224],"(x).":[225],"case":[228],"even":[234],"above":[238],"condition,":[239],"dual":[241],"code":[245],"has":[250],"optimal":[251],"minimum":[252],"distance.":[253]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":4}],"updated_date":"2026-04-03T22:45:19.894376","created_date":"2025-10-10T00:00:00"}
