{"id":"https://openalex.org/W2966402083","doi":"https://doi.org/10.1109/tit.2019.2932663","title":"Optimum Linear Codes With Support-Constrained Generator Matrices Over Small Fields","display_name":"Optimum Linear Codes With Support-Constrained Generator Matrices Over Small Fields","publication_year":2019,"publication_date":"2019-08-02","ids":{"openalex":"https://openalex.org/W2966402083","doi":"https://doi.org/10.1109/tit.2019.2932663","mag":"2966402083"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2019.2932663","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2019.2932663","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/A5059009269","display_name":"Hikmet Y\u0131ld\u0131z","orcid":"https://orcid.org/0000-0002-0891-3352"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hikmet Yildiz","raw_affiliation_strings":["Department of Electrical Engineering, California Institute of Technology, Pasadena, USA"],"raw_orcid":"https://orcid.org/0000-0002-0891-3352","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, California Institute of Technology, Pasadena, USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002430773","display_name":"Babak Hassibi","orcid":"https://orcid.org/0000-0002-1375-5838"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Babak Hassibi","raw_affiliation_strings":["Department of Electrical Engineering, California Institute of Technology, Pasadena, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, California Institute of Technology, Pasadena, USA","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I122411786"],"apc_list":null,"apc_paid":null,"fwci":0.4339,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.71824118,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"65","issue":"12","first_page":"7868","last_page":"7875"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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":0.9998000264167786,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9977999925613403,"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"}},{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9968000054359436,"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/conjecture","display_name":"Conjecture","score":0.6388412117958069},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.586374819278717},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5669482946395874},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5659810304641724},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.5324543118476868},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"Minimum distance","score":0.5061807036399841},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.49906253814697266},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4890771508216858},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4675057828426361},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4549824595451355},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4224073886871338},{"id":"https://openalex.org/keywords/generator-matrix","display_name":"Generator matrix","score":0.4121026396751404},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2686876058578491},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2646338939666748},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.2011221945285797},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1608370840549469},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.15468353033065796},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.09888285398483276},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0785137414932251},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.07061350345611572}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6388412117958069},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.586374819278717},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5669482946395874},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5659810304641724},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.5324543118476868},{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.5061807036399841},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.49906253814697266},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4890771508216858},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4675057828426361},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4549824595451355},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4224073886871338},{"id":"https://openalex.org/C1842014","wikidata":"https://www.wikidata.org/wiki/Q1502046","display_name":"Generator matrix","level":3,"score":0.4121026396751404},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2686876058578491},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2646338939666748},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.2011221945285797},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1608370840549469},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.15468353033065796},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09888285398483276},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0785137414932251},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.07061350345611572},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2019.2932663","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2019.2932663","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:authors.library.caltech.edu:97900","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20190814-151834005","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"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"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/668615","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/668615","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah 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/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"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/G2513274928","display_name":null,"funder_award_id":"CCF-1409204","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"},{"id":"https://openalex.org/G7130590601","display_name":null,"funder_award_id":"CCF-1018927","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"},{"id":"https://openalex.org/G8021919693","display_name":null,"funder_award_id":"CCF-1423663","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"},{"id":"https://openalex.org/G8673199588","display_name":null,"funder_award_id":"CNS-0932428","funder_id":"https://openalex.org/F4320337388","funder_display_name":"Division of Computer and Network Systems"}],"funders":[{"id":"https://openalex.org/F4320308258","display_name":"Qualcomm","ror":"https://ror.org/002zrf773"},{"id":"https://openalex.org/F4320322320","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38"},{"id":"https://openalex.org/F4320332375","display_name":"Jet Propulsion Laboratory","ror":"https://ror.org/027k65916"},{"id":"https://openalex.org/F4320337387","display_name":"Division of Computing and Communication Foundations","ror":"https://ror.org/01mng8331"},{"id":"https://openalex.org/F4320337388","display_name":"Division of Computer and Network Systems","ror":"https://ror.org/02rdzmk74"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1715633553","https://openalex.org/W1990732312","https://openalex.org/W1992741808","https://openalex.org/W1997044393","https://openalex.org/W2022619326","https://openalex.org/W2028758503","https://openalex.org/W2045717636","https://openalex.org/W2050536468","https://openalex.org/W2089857193","https://openalex.org/W2127064821","https://openalex.org/W2144181355","https://openalex.org/W2295155926","https://openalex.org/W2545678533","https://openalex.org/W2949916492","https://openalex.org/W2962854712","https://openalex.org/W2962949969","https://openalex.org/W2963439874","https://openalex.org/W2963779977","https://openalex.org/W2963801714","https://openalex.org/W2963843008","https://openalex.org/W2964144344","https://openalex.org/W2990109004","https://openalex.org/W3100004208","https://openalex.org/W3108043981","https://openalex.org/W4242513788","https://openalex.org/W6760815500"],"related_works":["https://openalex.org/W2766104912","https://openalex.org/W4298198176","https://openalex.org/W4300694038","https://openalex.org/W2085096159","https://openalex.org/W1989316102","https://openalex.org/W4322759337","https://openalex.org/W2099349446","https://openalex.org/W2740334431","https://openalex.org/W4212808623","https://openalex.org/W3099524591"],"abstract_inverted_index":{"We":[0,26],"consider":[1],"the":[2,13,23,29,49,56,82,110,114],"problem":[3],"of":[4,11,39,43,105],"designing":[5],"optimal":[6,87],"linear":[7],"codes":[8],"(in":[9],"terms":[10],"having":[12],"largest":[14,30],"minimum":[15,31,51,69],"distance)":[16],"subject":[17],"to":[18],"a":[19,37,40,103],"support":[20],"constraint":[21],"on":[22],"generator":[24,79],"matrix.":[25],"show":[27],"that":[28],"distance":[32,70],"can":[33],"be":[34],"achieved":[35],"by":[36],"subcode":[38],"Reed\u2013Solomon":[41],"code":[42,57,88],"small":[44],"field":[45,92],"size":[46,93],"and":[47,67],"with":[48,81],"same":[50],"distance.":[52],"In":[53],"particular,":[54],"if":[55],"has":[58],"length":[59],"<inline-formula":[60,71,94],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[61,72,95],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[62,73,96],"<tex-math":[63,74,97],"notation=\"LaTeX\">$n$":[64],"</tex-math></inline-formula>":[65,76,100],",":[66],"maximum":[68],"notation=\"LaTeX\">$d$":[75],"(over":[77],"all":[78],"matrices":[80],"given":[83],"support),":[84],"then":[85],"an":[86],"exists":[89],"for":[90],"any":[91],"notation=\"LaTeX\">$q\\geq":[98],"2n-d$":[99],".":[101],"As":[102],"by-product":[104],"this":[106],"result,":[107],"we":[108],"settle":[109],"GM\u2013MDS":[111],"conjecture":[112],"in":[113],"affirmative.":[115]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}