{"id":"https://openalex.org/W3170844331","doi":"https://doi.org/10.1109/tit.2021.3087082","title":"Shortened Linear Codes Over Finite Fields","display_name":"Shortened Linear Codes Over Finite Fields","publication_year":2021,"publication_date":"2021-06-08","ids":{"openalex":"https://openalex.org/W3170844331","doi":"https://doi.org/10.1109/tit.2021.3087082","mag":"3170844331"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2021.3087082","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3087082","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/A5074474523","display_name":"Yang Liu","orcid":"https://orcid.org/0000-0002-8928-8674"},"institutions":[{"id":"https://openalex.org/I110109458","display_name":"Tianjin University of Commerce","ror":"https://ror.org/02b6amy98","country_code":"CN","type":"education","lineage":["https://openalex.org/I110109458"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang Liu","raw_affiliation_strings":["College of Mathematics and Information Science, Tianjin University of Commerce, Tianjin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Tianjin University of Commerce, Tianjin, China","institution_ids":["https://openalex.org/I110109458"]}]},{"author_position":"middle","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":["The Hong Kong University of Science and Technology, Hong Kong, SAR, China"],"raw_orcid":"https://orcid.org/0000-0001-9392-9860","affiliations":[{"raw_affiliation_string":"The Hong Kong University of Science and Technology, Hong Kong, SAR, China","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054829854","display_name":"Chunming Tang","orcid":"https://orcid.org/0000-0001-9599-851X"},"institutions":[{"id":"https://openalex.org/I16351329","display_name":"China West Normal University","ror":"https://ror.org/04s99y476","country_code":"CN","type":"education","lineage":["https://openalex.org/I16351329"]},{"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":["CN","HK"],"is_corresponding":false,"raw_author_name":"Chunming Tang","raw_affiliation_strings":["School of Mathematics and Information, China West Normal University, Nanchong, China","The Hong Kong University of Science and Technology, Hong Kong, SAR, China"],"raw_orcid":"https://orcid.org/0000-0001-9599-851X","affiliations":[{"raw_affiliation_string":"School of Mathematics and Information, China West Normal University, Nanchong, China","institution_ids":["https://openalex.org/I16351329"]},{"raw_affiliation_string":"The Hong Kong University of Science and Technology, Hong Kong, SAR, China","institution_ids":["https://openalex.org/I200769079"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7987,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.91985666,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"67","issue":"8","first_page":"5119","last_page":"5132"},"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":0.9725000262260437,"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":0.9710000157356262,"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/puncturing","display_name":"Puncturing","score":0.8583027124404907},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.7750348448753357},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.7537415027618408},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.6740094423294067},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.5300374031066895},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5080306529998779},{"id":"https://openalex.org/keywords/reed\u2013muller-code","display_name":"Reed\u2013Muller code","score":0.5041693449020386},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.4531451165676117},{"id":"https://openalex.org/keywords/tornado-code","display_name":"Tornado code","score":0.4505760967731476},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.43264269828796387},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4122297465801239},{"id":"https://openalex.org/keywords/turbo-code","display_name":"Turbo code","score":0.4108516275882721},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38175198435783386},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3584449589252472},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.11082372069358826},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0665375292301178}],"concepts":[{"id":"https://openalex.org/C2778808095","wikidata":"https://www.wikidata.org/wiki/Q3899825","display_name":"Puncturing","level":2,"score":0.8583027124404907},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.7750348448753357},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.7537415027618408},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.6740094423294067},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.5300374031066895},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5080306529998779},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.5041693449020386},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.4531451165676117},{"id":"https://openalex.org/C65058987","wikidata":"https://www.wikidata.org/wiki/Q7826005","display_name":"Tornado code","level":5,"score":0.4505760967731476},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.43264269828796387},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4122297465801239},{"id":"https://openalex.org/C114504821","wikidata":"https://www.wikidata.org/wiki/Q2164281","display_name":"Turbo code","level":3,"score":0.4108516275882721},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38175198435783386},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3584449589252472},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.11082372069358826},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0665375292301178}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2021.3087082","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3087082","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:repository.hkust.edu.hk:1783.1-112243","is_oa":false,"landing_page_url":"http://lbdiscover.ust.hk/uresolver?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rfr_id=info:sid/HKUST:SPI&rft.genre=article&rft.issn=0018-9448&rft.volume=v. 67&rft.issue=(8)&rft.date=2021&rft.spage=5119&rft.aulast=Liu&rft.aufirst=Y.&rft.atitle=Shortened+Linear+Codes+over+Finite+Fields&rft.title=IEEE+Transactions+on+Information+Theory","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"},{"id":"pmh:oai:repository.ust.hk:1783.1-112243","is_oa":false,"landing_page_url":"http://repository.ust.hk/ir/Record/1783.1-112243","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":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1220597040","display_name":null,"funder_award_id":"16301020","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G2740439006","display_name":null,"funder_award_id":"11801414","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3615373735","display_name":null,"funder_award_id":"11701140","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G393080029","display_name":null,"funder_award_id":"CXTD2014-4","funder_id":"https://openalex.org/F4320324420","funder_display_name":"China West Normal University"},{"id":"https://openalex.org/G5072621123","display_name":null,"funder_award_id":"11871058","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6668725646","display_name":null,"funder_award_id":"14E013","funder_id":"https://openalex.org/F4320324420","funder_display_name":"China West Normal University"},{"id":"https://openalex.org/G7435862769","display_name":null,"funder_award_id":"A2019210223","funder_id":"https://openalex.org/F4320322163","funder_display_name":"Natural Science Foundation of Hebei Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321592","display_name":"Research Grants Council, University Grants Committee","ror":"https://ror.org/00djwmt25"},{"id":"https://openalex.org/F4320322163","display_name":"Natural Science Foundation of Hebei Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324420","display_name":"China West Normal University","ror":"https://ror.org/04s99y476"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W121517661","https://openalex.org/W1559343931","https://openalex.org/W1606480398","https://openalex.org/W1971640811","https://openalex.org/W1989168989","https://openalex.org/W1998253191","https://openalex.org/W2004166394","https://openalex.org/W2008721293","https://openalex.org/W2009324029","https://openalex.org/W2015337464","https://openalex.org/W2032078069","https://openalex.org/W2052900991","https://openalex.org/W2053535783","https://openalex.org/W2056890992","https://openalex.org/W2074099966","https://openalex.org/W2093749300","https://openalex.org/W2101226255","https://openalex.org/W2113800264","https://openalex.org/W2123499731","https://openalex.org/W2165062870","https://openalex.org/W2184646023","https://openalex.org/W2536942729","https://openalex.org/W2619359832","https://openalex.org/W2808199594","https://openalex.org/W2808611543","https://openalex.org/W2950788636","https://openalex.org/W2963030145","https://openalex.org/W2996205462","https://openalex.org/W2996995381","https://openalex.org/W4206775542","https://openalex.org/W4249150173","https://openalex.org/W4294525775","https://openalex.org/W6604926450","https://openalex.org/W6728513803","https://openalex.org/W6738540716"],"related_works":["https://openalex.org/W1977908590","https://openalex.org/W2943247777","https://openalex.org/W3170844331","https://openalex.org/W4235655084","https://openalex.org/W77726617","https://openalex.org/W4285666907","https://openalex.org/W1966899942","https://openalex.org/W2049979688","https://openalex.org/W2949741717","https://openalex.org/W2155439537"],"abstract_inverted_index":{"The":[0,79,95],"puncturing":[1,28,56],"and":[2,33,68,113],"shortening":[3,63],"techniques":[4],"are":[5,70,125,138],"two":[6],"important":[7],"approaches":[8],"to":[9,86,99],"constructing":[10],"new":[11],"linear":[12,38,46,77,93],"codes":[13,39,47,103,121,146],"from":[14,141],"old":[15],"ones.":[16],"In":[17],"the":[18,27,55,62,105,144],"past":[19],"70":[20],"years,":[21],"a":[22,72,131],"lot":[23],"of":[24,45,82,104,118,136,143],"progress":[25],"on":[26,36,61,75],"technique":[29,64],"has":[30,65],"been":[31,41,52,66],"made,":[32],"many":[34],"works":[35],"punctured":[37],"have":[40,51],"done.":[42],"Many":[43],"families":[44,117,135],"with":[48,54],"interesting":[49],"parameters":[50],"obtained":[53],"technique.":[57],"However,":[58],"little":[59],"research":[60],"done":[67],"there":[69],"only":[71],"handful":[73],"references":[74],"shortened":[76,92,102,120,145],"codes.":[78,94,115],"first":[80],"objective":[81,97],"this":[83,128,149],"paper":[84],"is":[85,98],"prove":[87],"some":[88,101,110,142],"general":[89],"theory":[90],"for":[91],"second":[96],"study":[100],"Hamming":[106],"codes,":[107,109,112],"Simplex":[108],"Reed-Muller":[111],"ovoid":[114],"Eleven":[116],"optimal":[119],"over":[122],"finite":[123],"fields":[124],"presented":[126,147],"in":[127,148],"paper.":[129,150],"As":[130],"byproduct,":[132],"five":[133],"infinite":[134],"2-designs":[137],"also":[139],"constructed":[140]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}