{"id":"https://openalex.org/W4414110815","doi":"https://doi.org/10.1109/tit.2025.3608579","title":"Optimal Linear Codes From Duals of Punctured Concatenated Codes","display_name":"Optimal Linear Codes From Duals of Punctured Concatenated Codes","publication_year":2025,"publication_date":"2025-09-10","ids":{"openalex":"https://openalex.org/W4414110815","doi":"https://doi.org/10.1109/tit.2025.3608579"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2025.3608579","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3608579","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/A5064767096","display_name":"Guanghui Li","orcid":"https://orcid.org/0000-0001-8856-2953"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guanghui Li","raw_affiliation_strings":["School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001858160","display_name":"Gaojun Luo","orcid":"https://orcid.org/0000-0003-1482-4783"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gaojun Luo","raw_affiliation_strings":["School of Mathematics and the Key Laboratory of Mathematical Modeling and High Performance Computing of Air Vehicles, MIIT, Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China","School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and the Key Laboratory of Mathematical Modeling and High Performance Computing of Air Vehicles, MIIT, Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China","institution_ids":["https://openalex.org/I9842412"]},{"raw_affiliation_string":"School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011952918","display_name":"Yijun Cui","orcid":"https://orcid.org/0000-0002-6262-2329"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yijun Cui","raw_affiliation_strings":["College of Integrated Circuits, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"College of Integrated Circuits, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026635882","display_name":"Xiwang Cao","orcid":"https://orcid.org/0000-0002-6950-8588"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiwang Cao","raw_affiliation_strings":["School of Mathematics and the Key Laboratory of Mathematical Modeling and High Performance Computing of Air Vehicles, MIIT, Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China","School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and the Key Laboratory of Mathematical Modeling and High Performance Computing of Air Vehicles, MIIT, Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China","institution_ids":["https://openalex.org/I9842412"]},{"raw_affiliation_string":"School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063268716","display_name":"San Ling","orcid":"https://orcid.org/0000-0002-1978-3557"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"San Ling","raw_affiliation_strings":["School of Physical and Mathematical Sciences, Nanyang Technological University, Jurong West, Singapore","School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore"],"affiliations":[{"raw_affiliation_string":"School of Physical and Mathematical Sciences, Nanyang Technological University, Jurong West, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5064767096"],"corresponding_institution_ids":["https://openalex.org/I9842412"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13185332,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"71","issue":"12","first_page":"9482","last_page":"9495"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9973999857902527,"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":0.9973999857902527,"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":0.9749000072479248,"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":0.9667999744415283,"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/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.7443000078201294},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.6978999972343445},{"id":"https://openalex.org/keywords/dual-polyhedron","display_name":"Dual polyhedron","score":0.6517000198364258},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.576200008392334},{"id":"https://openalex.org/keywords/polynomial-code","display_name":"Polynomial code","score":0.5439000129699707},{"id":"https://openalex.org/keywords/puncturing","display_name":"Puncturing","score":0.536300003528595},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5128999948501587},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5097000002861023},{"id":"https://openalex.org/keywords/constant-weight-code","display_name":"Constant-weight code","score":0.5065000057220459}],"concepts":[{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.7443000078201294},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.6978999972343445},{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.6517000198364258},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6414999961853027},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.576200008392334},{"id":"https://openalex.org/C39635130","wikidata":"https://www.wikidata.org/wiki/Q7226636","display_name":"Polynomial code","level":5,"score":0.5439000129699707},{"id":"https://openalex.org/C2778808095","wikidata":"https://www.wikidata.org/wiki/Q3899825","display_name":"Puncturing","level":2,"score":0.536300003528595},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5128999948501587},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5097000002861023},{"id":"https://openalex.org/C197242373","wikidata":"https://www.wikidata.org/wiki/Q5163613","display_name":"Constant-weight code","level":5,"score":0.5065000057220459},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.4864000082015991},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4796999990940094},{"id":"https://openalex.org/C73666251","wikidata":"https://www.wikidata.org/wiki/Q5310189","display_name":"Dual code","level":5,"score":0.47760000824928284},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.45080000162124634},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.44179999828338623},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.396699994802475},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.3874000012874603},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.375},{"id":"https://openalex.org/C70992990","wikidata":"https://www.wikidata.org/wiki/Q1681587","display_name":"Systematic code","level":4,"score":0.374099999666214},{"id":"https://openalex.org/C2096984","wikidata":"https://www.wikidata.org/wiki/Q245464","display_name":"Cyclic code","level":5,"score":0.35089999437332153},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3450999855995178},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.3400000035762787},{"id":"https://openalex.org/C20079647","wikidata":"https://www.wikidata.org/wiki/Q1278039","display_name":"Prefix code","level":5,"score":0.33090001344680786},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32330000400543213},{"id":"https://openalex.org/C157899210","wikidata":"https://www.wikidata.org/wiki/Q1395022","display_name":"Convolutional code","level":3,"score":0.29280000925064087},{"id":"https://openalex.org/C114504821","wikidata":"https://www.wikidata.org/wiki/Q2164281","display_name":"Turbo code","level":3,"score":0.28130000829696655},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C3427991","wikidata":"https://www.wikidata.org/wiki/Q651426","display_name":"Group code","level":5,"score":0.26510000228881836},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2540000081062317},{"id":"https://openalex.org/C108509264","wikidata":"https://www.wikidata.org/wiki/Q5420758","display_name":"Expander code","level":5,"score":0.2540000081062317},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2524999976158142}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2025.3608579","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3608579","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1471103927","https://openalex.org/W1933802677","https://openalex.org/W1969945141","https://openalex.org/W1973483608","https://openalex.org/W2039170351","https://openalex.org/W2048316651","https://openalex.org/W2094825109","https://openalex.org/W2123695891","https://openalex.org/W2137451425","https://openalex.org/W2566390621","https://openalex.org/W2612743620","https://openalex.org/W2807159747","https://openalex.org/W2888200295","https://openalex.org/W2962899399","https://openalex.org/W2963051664","https://openalex.org/W2963907012","https://openalex.org/W2979768263","https://openalex.org/W3013959785","https://openalex.org/W3092468373","https://openalex.org/W3145381334","https://openalex.org/W3168938245","https://openalex.org/W3172180125","https://openalex.org/W3189288785","https://openalex.org/W3194802667","https://openalex.org/W4205447848","https://openalex.org/W4206775542","https://openalex.org/W4213287502","https://openalex.org/W4248289108","https://openalex.org/W4288646626","https://openalex.org/W4387020221","https://openalex.org/W4388286203","https://openalex.org/W4393066233","https://openalex.org/W4394012102","https://openalex.org/W4398160375","https://openalex.org/W4401178644","https://openalex.org/W4403210342","https://openalex.org/W4406795103"],"related_works":["https://openalex.org/W135568846","https://openalex.org/W2151857680","https://openalex.org/W2460434904","https://openalex.org/W1534925464","https://openalex.org/W1798117689","https://openalex.org/W2209506458","https://openalex.org/W2977752192","https://openalex.org/W58580312","https://openalex.org/W832867880","https://openalex.org/W2747534004"],"abstract_inverted_index":{"A":[0],"code":[1,7,17,48,57,97,151],"is":[2],"called":[3],"a":[4,15,92],"punctured":[5],"concatenated":[6,16],"if":[8],"it":[9],"can":[10],"be":[11,49,129],"obtained":[12],"by":[13,90,147],"puncturing":[14],"at":[18],"suitable":[19],"coordinates.":[20],"Based":[21],"on":[22],"this":[23,43],"new":[24],"concept,":[25],"we":[26,111,165],"construct":[27,166],"several":[28],"classes":[29,114],"of":[30,115,123,169,177],"optimal":[31,34],"or":[32],"almost":[33,188],"linear":[35,56,116,170],"codes.":[36,171],"There":[37],"are":[38,126,180,187],"two":[39,113],"major":[40],"contributions":[41],"in":[42],"paper.":[44],"Let":[45],"the":[46,60,87,108,134,138,162,193],"inner":[47],"an":[50,149],"[<italic":[51],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[52,54,64,68,70,73,75,82,84,103,105,143,157,159],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n,m</i>]<sub":[53],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><i>q</i></sub>":[55],"derived":[58],"from":[59],"defining":[61],"set":[62],"<italic":[63,72,81,142],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">D</i>":[65],"=":[66,145],"{<italic":[67],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">d</i><sub":[69,74,83],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>,":[71],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>,":[76],".":[77,78,79],",":[80],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><i>n</i></sub>}.":[85],"On":[86,137],"one":[88],"hand,":[89,140],"employing":[91],"maximum":[93],"distance":[94],"separable":[95],"(MDS)":[96],"with":[98,118,131,152,190],"dimension":[99,153],"2":[100],"over":[101,155],"F<sub":[102,156],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><i>q</i></sub><sup":[104],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><i>m</i></sup>":[106,160],"as":[107,161],"outer":[109,163],"code,":[110,164],"propose":[112],"codes":[117,125,179,186],"few":[119],"weights.":[120],"The":[121,172],"duals":[122],"these":[124,178],"shown":[127],"to":[128,133,192],"dimension-optimal":[130],"respect":[132,191],"sphere-packing":[135,194],"bound.":[136,195],"other":[139],"let":[141],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">q</i>":[144],"2,":[146],"choosing":[148],"MDS":[150],"3":[154],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub><sup":[158],"another":[167],"class":[168],"parameters":[173],"and":[174],"weight":[175],"distributions":[176],"completely":[181],"determined.":[182],"Furthermore,":[183],"their":[184],"dual":[185],"distance-optimal":[189]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-10T00:00:00"}
