{"id":"https://openalex.org/W3201874919","doi":"https://doi.org/10.1587/transfun.2021eap1062","title":"Construction of Two Classes of Minimal Binary Linear Codes Based on Boolean Function","display_name":"Construction of Two Classes of Minimal Binary Linear Codes Based on Boolean Function","publication_year":2021,"publication_date":"2021-09-29","ids":{"openalex":"https://openalex.org/W3201874919","doi":"https://doi.org/10.1587/transfun.2021eap1062","mag":"3201874919"},"language":"en","primary_location":{"id":"doi:10.1587/transfun.2021eap1062","is_oa":false,"landing_page_url":"https://doi.org/10.1587/transfun.2021eap1062","pdf_url":null,"source":{"id":"https://openalex.org/S166990724","display_name":"IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences","issn_l":"0916-8508","issn":["0916-8508","1745-1337"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4320800604","host_organization_name":"Institute of Electronics, Information and Communication Engineers","host_organization_lineage":["https://openalex.org/P4320800604"],"host_organization_lineage_names":["Institute of Electronics, Information and Communication Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences","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/A5102460018","display_name":"Jiawei Du","orcid":"https://orcid.org/0000-0002-7186-6632"},"institutions":[{"id":"https://openalex.org/I5343935","display_name":"Guilin University of Electronic Technology","ror":"https://ror.org/05arjae42","country_code":"CN","type":"education","lineage":["https://openalex.org/I5343935"]},{"id":"https://openalex.org/I68986083","display_name":"Northwest Normal University","ror":"https://ror.org/00gx3j908","country_code":"CN","type":"education","lineage":["https://openalex.org/I68986083"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiawei DU","raw_affiliation_strings":["College of Mathematics and Statistics, Northwest Normal University","Guangxi Key Laboratory of Cryptography and Information Security, Guilin University of Electronic Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Northwest Normal University","institution_ids":["https://openalex.org/I68986083"]},{"raw_affiliation_string":"Guangxi Key Laboratory of Cryptography and Information Security, Guilin University of Electronic Technology","institution_ids":["https://openalex.org/I5343935"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101507366","display_name":"Xiaoni Du","orcid":"https://orcid.org/0000-0003-3997-7196"},"institutions":[{"id":"https://openalex.org/I68986083","display_name":"Northwest Normal University","ror":"https://ror.org/00gx3j908","country_code":"CN","type":"education","lineage":["https://openalex.org/I68986083"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoni DU","raw_affiliation_strings":["College of Mathematics and Statistics, Northwest Normal University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Northwest Normal University","institution_ids":["https://openalex.org/I68986083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033792776","display_name":"Wengang Jin","orcid":null},"institutions":[{"id":"https://openalex.org/I68986083","display_name":"Northwest Normal University","ror":"https://ror.org/00gx3j908","country_code":"CN","type":"education","lineage":["https://openalex.org/I68986083"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wengang JIN","raw_affiliation_strings":["College of Mathematics and Statistics, Northwest Normal University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Northwest Normal University","institution_ids":["https://openalex.org/I68986083"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022405179","display_name":"Yingzhong Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I68986083","display_name":"Northwest Normal University","ror":"https://ror.org/00gx3j908","country_code":"CN","type":"education","lineage":["https://openalex.org/I68986083"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yingzhong ZHANG","raw_affiliation_strings":["College of Mathematics and Statistics, Northwest Normal University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Northwest Normal University","institution_ids":["https://openalex.org/I68986083"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13755623,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"E105.A","issue":"4","first_page":"689","last_page":"693"},"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":0.9990000128746033,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9970999956130981,"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/boolean-function","display_name":"Boolean function","score":0.6668250560760498},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.6657501459121704},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.6133082509040833},{"id":"https://openalex.org/keywords/weight-distribution","display_name":"Weight distribution","score":0.5987161993980408},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.5552654266357422},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.54966801404953},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.5269884467124939},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5025901794433594},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.49791383743286133},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.48492103815078735},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4822614789009094},{"id":"https://openalex.org/keywords/secret-sharing","display_name":"Secret sharing","score":0.47831347584724426},{"id":"https://openalex.org/keywords/reed\u2013muller-code","display_name":"Reed\u2013Muller code","score":0.4737435281276703},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.431535542011261},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.387622207403183},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33575016260147095},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25765490531921387},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.0634617805480957}],"concepts":[{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.6668250560760498},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.6657501459121704},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.6133082509040833},{"id":"https://openalex.org/C25432639","wikidata":"https://www.wikidata.org/wiki/Q3711790","display_name":"Weight distribution","level":2,"score":0.5987161993980408},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5552654266357422},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.54966801404953},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.5269884467124939},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5025901794433594},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.49791383743286133},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.48492103815078735},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4822614789009094},{"id":"https://openalex.org/C3087436","wikidata":"https://www.wikidata.org/wiki/Q1386603","display_name":"Secret sharing","level":3,"score":0.47831347584724426},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.4737435281276703},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.431535542011261},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.387622207403183},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33575016260147095},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25765490531921387},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0634617805480957},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1587/transfun.2021eap1062","is_oa":false,"landing_page_url":"https://doi.org/10.1587/transfun.2021eap1062","pdf_url":null,"source":{"id":"https://openalex.org/S166990724","display_name":"IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences","issn_l":"0916-8508","issn":["0916-8508","1745-1337"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4320800604","host_organization_name":"Institute of Electronics, Information and Communication Engineers","host_organization_lineage":["https://openalex.org/P4320800604"],"host_organization_lineage_names":["Institute of Electronics, Information and Communication Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4300000071525574,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1471103927","https://openalex.org/W1587687098","https://openalex.org/W1969945141","https://openalex.org/W1973400298","https://openalex.org/W1978208015","https://openalex.org/W2028984939","https://openalex.org/W2032685643","https://openalex.org/W2098933212","https://openalex.org/W2120756519","https://openalex.org/W2163834165","https://openalex.org/W2792402434","https://openalex.org/W4245633009"],"related_works":["https://openalex.org/W3045580795","https://openalex.org/W2920889620","https://openalex.org/W4312936811","https://openalex.org/W2952098968","https://openalex.org/W3021758908","https://openalex.org/W1667411252","https://openalex.org/W2161125858","https://openalex.org/W2579163092","https://openalex.org/W2952431332","https://openalex.org/W2996335208"],"abstract_inverted_index":{"Linear":[0],"codes":[1,45,63,73],"with":[2,27,46,102],"a":[3,22,88],"few-weight":[4],"have":[5],"important":[6],"applications":[7],"in":[8],"combinatorial":[9],"design,":[10],"strongly":[11],"regular":[12],"graphs":[13],"and":[14,33,58,76,84,92],"cryptography.":[15],"In":[16],"this":[17],"paper,":[18],"we":[19,39],"first":[20],"construct":[21],"class":[23],"of":[24,43,61,70,116],"Boolean":[25],"functions":[26],"at":[28,47],"most":[29,48],"five-valued":[30],"Walsh":[31],"spectra,":[32],"determine":[34],"their":[35],"spectrum":[36],"distribution.":[37],"Then,":[38],"derive":[40],"two":[41],"classes":[42],"linear":[44],"six-weight":[49],"from":[50],"the":[51,55,62,71,85,114],"new":[52,72],"functions.":[53],"Meanwhile,":[54],"length,":[56],"dimension":[57],"weight":[59],"distributions":[60],"are":[64,74,110],"obtained.":[65],"Results":[66],"show":[67],"that":[68],"both":[69],"minimal":[75,82,90],"among":[77],"them,":[78],"one":[79],"is":[80,87],"wide":[81],"code":[83,91],"other":[86],"narrow":[89],"thus":[93],"can":[94],"be":[95],"used":[96,111],"to":[97,112],"design":[98],"secret":[99],"sharing":[100],"scheme":[101],"good":[103],"access":[104],"structures.":[105],"Finally,":[106],"some":[107],"Magma":[108],"programs":[109],"verify":[113],"correctness":[115],"our":[117],"results.":[118]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
