{"id":"https://openalex.org/W2972166002","doi":"https://doi.org/10.1109/access.2019.2939153","title":"A Class of Linear Codes and Their Complete Weight Enumerators","display_name":"A Class of Linear Codes and Their Complete Weight Enumerators","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2972166002","doi":"https://doi.org/10.1109/access.2019.2939153","mag":"2972166002"},"language":"en","primary_location":{"id":"doi:10.1109/access.2019.2939153","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2939153","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08822968.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08822968.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054494046","display_name":"Xiangli Kong","orcid":null},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiangli Kong","raw_affiliation_strings":["School of Mathematical Sciences, Qufu Normal University, Jining, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Qufu Normal University, Jining, China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033644023","display_name":"Shudi Yang","orcid":"https://orcid.org/0000-0003-1536-4627"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shudi Yang","raw_affiliation_strings":["School of Mathematical Sciences, Qufu Normal University, Jining, China"],"raw_orcid":"https://orcid.org/0000-0003-1536-4627","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Qufu Normal University, Jining, China","institution_ids":["https://openalex.org/I202126657"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5054494046"],"corresponding_institution_ids":["https://openalex.org/I202126657"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.2904,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.66985694,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"7","issue":null,"first_page":"127833","last_page":"127838"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9940999746322632,"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":0.9878000020980835,"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/notation","display_name":"Notation","score":0.6494563817977905},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5021727085113525},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45363056659698486},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37982624769210815},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33624976873397827},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29407837986946106},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1921045482158661},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.16187959909439087}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6494563817977905},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5021727085113525},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45363056659698486},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37982624769210815},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33624976873397827},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29407837986946106},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1921045482158661},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.16187959909439087}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2019.2939153","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2939153","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08822968.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:df01ae843c71417fbe58ec54421d90e7","is_oa":false,"landing_page_url":"https://doaj.org/article/df01ae843c71417fbe58ec54421d90e7","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 7, Pp 127833-127838 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2019.2939153","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2939153","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08822968.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G10279494","display_name":null,"funder_award_id":"ZR2016AM04","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1272789696","display_name":null,"funder_award_id":"11801303","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G193913955","display_name":null,"funder_award_id":"ZR2019QA016","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G5946210596","display_name":null,"funder_award_id":"ZR2016AM04","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G6129197603","display_name":null,"funder_award_id":"11701317","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G896654614","display_name":null,"funder_award_id":"11971497","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/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2972166002.pdf","grobid_xml":"https://content.openalex.org/works/W2972166002.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W809948269","https://openalex.org/W840046362","https://openalex.org/W1606480398","https://openalex.org/W1969945141","https://openalex.org/W1977461479","https://openalex.org/W2001553361","https://openalex.org/W2011063323","https://openalex.org/W2012525201","https://openalex.org/W2029487152","https://openalex.org/W2030171660","https://openalex.org/W2058193976","https://openalex.org/W2080824882","https://openalex.org/W2082432022","https://openalex.org/W2098933212","https://openalex.org/W2099197486","https://openalex.org/W2101226255","https://openalex.org/W2120756519","https://openalex.org/W2140576949","https://openalex.org/W2172014365","https://openalex.org/W2200841142","https://openalex.org/W2214330823","https://openalex.org/W2233046555","https://openalex.org/W2560684815","https://openalex.org/W2560746398","https://openalex.org/W2566658350","https://openalex.org/W2572231742","https://openalex.org/W2604096566","https://openalex.org/W2741335303","https://openalex.org/W2770399699","https://openalex.org/W2903472328","https://openalex.org/W2962947453","https://openalex.org/W2963650779","https://openalex.org/W3103559917","https://openalex.org/W3103820093","https://openalex.org/W3147043509","https://openalex.org/W4206775542","https://openalex.org/W6792971814"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2504004674","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298"],"abstract_inverted_index":{"Linear":[0],"codes":[1,170,215,222],"may":[2],"have":[3],"a":[4,159,217],"few":[5,218],"weights":[6],"if":[7],"their":[8,205],"defining":[9],"sets":[10],"are":[11,223],"chosen":[12],"properly.":[13],"Let":[14],"<inline-formula":[15,23,37,48,57,65,89,97,106,119,137,162,173,188],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[16,24,38,49,58,66,75,80,90,98,107,120,138,163,174,189],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[17,25,39,50,59,67,91,99,108,121,139,164,175,190],"<tex-math":[18,26,40,51,60,68,92,100,109,122,140,165,176,191],"notation=\"LaTeX\">$s":[19],"$":[20,28,42,53,62,70,145],"</tex-math></inline-formula>":[21,29,43,54,63,71,95,103,112,134,146,167,185,200],"and":[22,44,72],"notation=\"LaTeX\">$t":[27],"be":[30,83],"positive":[31],"integers.":[32],"For":[33],"an":[34,45],"odd":[35],"prime":[36],"notation=\"LaTeX\">$p":[41],"even":[46],"integer":[47],"notation=\"LaTeX\">$m":[52],",":[55,64,135,186],"let":[56],"notation=\"LaTeX\">$q=p^{m}":[61],"notation=\"LaTeX\">$m=2s":[69],"Tr":[73,78],"<sub":[74,79],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><i>m</i></sub>":[76],"(resp.":[77,96],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><i>s</i></sub>":[81],")":[82,104],"the":[84,154],"absolute":[85],"trace":[86],"function":[87],"from":[88],"notation=\"LaTeX\">$\\mathbb":[93,101,110],"{F}_{q}$":[94],"{F}_{p^{s}}$":[102],"to":[105],"{F}_{p}$":[111],".":[113,147,201],"In":[114],"this":[115],"paper,":[116],"we":[117,152,203],"define":[118],"notation=\"LaTeX\">$D_{b}":[123],"=\\{":[124],"(x_{1},\\ldots,x_{t})\\in":[125],"\\mathbb":[126,143,183],"{F}_{q}^{t}":[127],"\\backslash":[128],"\\{(0,\\ldots,0)\\}:":[129],"\\mathrm":[130],"{Tr}_{m}":[131],"(x_{1}+\\cdots":[132],"+x_{t})=b\\}$":[133],"where":[136,187],"notation=\"LaTeX\">$b":[141],"\\in":[142],"{F}_{p}":[144],"By":[148],"employing":[149],"exponential":[150],"sums,":[151],"demonstrate":[153],"complete":[155],"weight":[156,206],"enumerators":[157,207],"of":[158,161],"class":[160],"notation=\"LaTeX\">$p$":[166],"-ary":[168],"linear":[169,214],"given":[171],"by":[172],"notation=\"LaTeX\">$C_{D_{b}":[177],"}=\\{\\mathsf":[178],"{c}(a_{1},":[179,193],"\\ldots,":[180,194],"a_{t}):":[181],"a_{1},\\ldots,a_{t}\\in":[182],"{F}_{p^{s}}\\}$":[184],"notation=\"LaTeX\">$\\mathsf":[192],"a_{t})=(\\mathrm":[195],"{Tr}_{s}(a_{1}x_{1}^{p^{s}+1}+\\cdots":[196],"+a_{t}x_{t}^{p^{s}+1}))_{(x_{1},\\ldots,x_{t})\\in":[197],"D_{b}":[198],"}$":[199],"Then":[202],"get":[204],"explicitly,":[208],"which":[209],"will":[210],"give":[211],"us":[212],"several":[213],"with":[216,225],"weights.":[219],"The":[220],"presented":[221],"suitable":[224],"applications":[226],"in":[227],"secret":[228],"sharing":[229],"schemes.":[230]},"counts_by_year":[{"year":2020,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
