{"id":"https://openalex.org/W4312887105","doi":"https://doi.org/10.3934/amc.2022081","title":"Generalized hamming weights of linear codes from cryptographic functions","display_name":"Generalized hamming weights of linear codes from cryptographic functions","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4312887105","doi":"https://doi.org/10.3934/amc.2022081"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2022081","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2022081","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=634609494cedfd00071dcb01","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/data/article/export-pdf?id=634609494cedfd00071dcb01","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073722882","display_name":"Kangquan Li","orcid":"https://orcid.org/0000-0002-6708-2309"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kangquan Li","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100353589","display_name":"Hao Chen","orcid":"https://orcid.org/0000-0002-7880-3394"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hao Chen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5071414491","display_name":"Longjiang Qu","orcid":"https://orcid.org/0000-0003-3506-5501"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Longjiang Qu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5073722882"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5552,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.73152496,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"16","issue":"4","first_page":"859","last_page":"877"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9713000059127808,"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":0.9693999886512756,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8952316045761108},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.7439841032028198},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.7429147362709045},{"id":"https://openalex.org/keywords/hamming-weight","display_name":"Hamming weight","score":0.5656935572624207},{"id":"https://openalex.org/keywords/hamming","display_name":"Hamming(7,4)","score":0.5016987323760986},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.49484628438949585},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.43247976899147034},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3746633529663086},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33912941813468933},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2073010802268982},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.1769210398197174},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.08220991492271423}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8952316045761108},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.7439841032028198},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.7429147362709045},{"id":"https://openalex.org/C63361517","wikidata":"https://www.wikidata.org/wiki/Q5645805","display_name":"Hamming weight","level":5,"score":0.5656935572624207},{"id":"https://openalex.org/C112932734","wikidata":"https://www.wikidata.org/wiki/Q2322550","display_name":"Hamming(7,4)","level":5,"score":0.5016987323760986},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.49484628438949585},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.43247976899147034},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3746633529663086},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33912941813468933},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2073010802268982},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.1769210398197174},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.08220991492271423}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2022081","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2022081","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=634609494cedfd00071dcb01","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/amc.2022081","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2022081","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=634609494cedfd00071dcb01","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4312887105.pdf","grobid_xml":"https://content.openalex.org/works/W4312887105.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2008960744","https://openalex.org/W2105471374","https://openalex.org/W1987803429","https://openalex.org/W2963549154","https://openalex.org/W2158117886","https://openalex.org/W2740543340","https://openalex.org/W1519122282","https://openalex.org/W1582340598","https://openalex.org/W2182731056","https://openalex.org/W2157753730"],"abstract_inverted_index":{"The":[0],"generalized":[1,42,96,116,193],"Hamming":[2,43,97,117,194],"weights":[3,78,98,118,195],"of":[4,20,28,99,119,135,142,161,169,196],"linear":[5,22,40,62,74,100,120,136,197],"codes":[6,63,75,101,121,137,198],"have":[7,79],"attracted":[8],"scholars'":[9],"attention":[10],"since":[11,53],"Wei":[12],"used":[13],"them":[14],"to":[15,38,90,113,187],"characterize":[16],"the":[17,25,46,50,95,115,123,148,153,167,192],"cryptography":[18],"performance":[19],"a":[21,58,110],"code":[23],"over":[24],"wire-tap":[26],"channel":[27],"type":[29],"II":[30],"in":[31,71],"1991.":[32],"Generally":[33],"speaking,":[34],"it":[35],"is":[36],"hard":[37],"determine":[39],"codes'":[41],"weights,":[44],"especially":[45],"weight":[47,133],"hierarchy.":[48],"On":[49],"other":[51],"hand,":[52],"Ding":[54],"and":[55,158,173],"Niederreiter":[56],"presented":[57],"generic":[59],"approach":[60],"toconstruct":[61],"with":[64,76],"good":[65],"properties":[66],"by":[67],"suitable":[68],"defining":[69,124],"sets":[70],"2007,":[72],"many":[73],"few":[77],"been":[80],"obtained":[81],"using":[82],"cryptographic":[83,103,200],"functions.":[84,201],"However,":[85],"there":[86],"does":[87],"not":[88],"seem":[89],"be":[91],"much":[92],"research":[93],"on":[94],"from":[102,122,138,199],"functions.In":[104],"this":[105,181],"paper,":[106],"we":[107],"first":[108],"provide":[109],"general":[111],"formula":[112],"compute":[114],"sets,":[125],"which":[126],"generalizes":[127],"several":[128],"known":[129],"results.":[130],"Next,":[131],"some":[132],"hierarchies":[134],"three":[139],"famous":[140],"classes":[141,160],"Bent":[143],"functions":[144,163],"(the":[145,164],"Maiorana-McFarland":[146,165],"class,":[147,166],"class":[149,154],"$":[150,155,170,172,174],"\\mathcal{PS}_{ap}":[151,171],"$,":[152],"H":[156,175],"$)":[157,176],"two":[159],"Semi-Bent":[162],"summation":[168],"are":[177],"considered.":[178],"We":[179],"hope":[180],"paper":[182],"can":[183],"attract":[184],"interested":[185],"scholars":[186],"find":[188],"more":[189],"results":[190],"about":[191]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}