{"id":"https://openalex.org/W2539039118","doi":"https://doi.org/10.1109/tit.2017.2755682","title":"Improved Constructions of Nested Code Pairs","display_name":"Improved Constructions of Nested Code Pairs","publication_year":2017,"publication_date":"2017-09-22","ids":{"openalex":"https://openalex.org/W2539039118","doi":"https://doi.org/10.1109/tit.2017.2755682","mag":"2539039118"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2017.2755682","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2755682","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1610.06363","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Carlos Galindo","orcid":"https://orcid.org/0000-0002-3908-4462"},"institutions":[{"id":"https://openalex.org/I10902133","display_name":"Universitat Jaume I","ror":"https://ror.org/02ws1xc11","country_code":"ES","type":"education","lineage":["https://openalex.org/I10902133"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Carlos Galindo","raw_affiliation_strings":["Instituto Universitario de Matem\u00e1ticas y Aplicaciones de Castell\u00f3n, Jaume I University, Castell\u00f3n de la Plana, Spain"],"raw_orcid":"https://orcid.org/0000-0002-3908-4462","affiliations":[{"raw_affiliation_string":"Instituto Universitario de Matem\u00e1ticas y Aplicaciones de Castell\u00f3n, Jaume I University, Castell\u00f3n de la Plana, Spain","institution_ids":["https://openalex.org/I10902133"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Olav Geil","orcid":"https://orcid.org/0000-0002-9666-3399"},"institutions":[{"id":"https://openalex.org/I891191580","display_name":"Aalborg University","ror":"https://ror.org/04m5j1k67","country_code":"DK","type":"education","lineage":["https://openalex.org/I891191580"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Olav Geil","raw_affiliation_strings":["Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark"],"raw_orcid":"https://orcid.org/0000-0002-9666-3399","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark","institution_ids":["https://openalex.org/I891191580"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Fernando Hernando","orcid":"https://orcid.org/0000-0002-9758-2152"},"institutions":[{"id":"https://openalex.org/I10902133","display_name":"Universitat Jaume I","ror":"https://ror.org/02ws1xc11","country_code":"ES","type":"education","lineage":["https://openalex.org/I10902133"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Fernando Hernando","raw_affiliation_strings":["Instituto Universitario de Matem\u00e1ticas y Aplicaciones de Castell\u00f3n, Jaume I University, Castell\u00f3n de la Plana, Spain"],"raw_orcid":"https://orcid.org/0000-0002-9758-2152","affiliations":[{"raw_affiliation_string":"Instituto Universitario de Matem\u00e1ticas y Aplicaciones de Castell\u00f3n, Jaume I University, Castell\u00f3n de la Plana, Spain","institution_ids":["https://openalex.org/I10902133"]}]},{"author_position":"last","author":{"id":null,"display_name":"Diego Ruano","orcid":"https://orcid.org/0000-0001-7304-0087"},"institutions":[{"id":"https://openalex.org/I891191580","display_name":"Aalborg University","ror":"https://ror.org/04m5j1k67","country_code":"DK","type":"education","lineage":["https://openalex.org/I891191580"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Diego Ruano","raw_affiliation_strings":["Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark"],"raw_orcid":"https://orcid.org/0000-0001-7304-0087","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark","institution_ids":["https://openalex.org/I891191580"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4458,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.86192737,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"64","issue":"4","first_page":"2444","last_page":"2459"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.5824999809265137,"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":0.5824999809265137,"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":0.1858000010251999,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.05990000069141388,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.6144999861717224},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.48840001225471497},{"id":"https://openalex.org/keywords/codimension","display_name":"Codimension","score":0.4668999910354614},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.42320001125335693},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.4153999984264374},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.38179999589920044},{"id":"https://openalex.org/keywords/polynomial-code","display_name":"Polynomial code","score":0.3571000099182129},{"id":"https://openalex.org/keywords/secret-sharing","display_name":"Secret sharing","score":0.33980000019073486}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6733999848365784},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.6144999861717224},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5388000011444092},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.48840001225471497},{"id":"https://openalex.org/C83979697","wikidata":"https://www.wikidata.org/wiki/Q1778247","display_name":"Codimension","level":2,"score":0.4668999910354614},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.42320001125335693},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.4153999984264374},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.396699994802475},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.38179999589920044},{"id":"https://openalex.org/C39635130","wikidata":"https://www.wikidata.org/wiki/Q7226636","display_name":"Polynomial code","level":5,"score":0.3571000099182129},{"id":"https://openalex.org/C3087436","wikidata":"https://www.wikidata.org/wiki/Q1386603","display_name":"Secret sharing","level":3,"score":0.33980000019073486},{"id":"https://openalex.org/C1306188","wikidata":"https://www.wikidata.org/wiki/Q4060687","display_name":"Nested loop join","level":2,"score":0.31299999356269836},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.3084999918937683},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29840001463890076},{"id":"https://openalex.org/C108509264","wikidata":"https://www.wikidata.org/wiki/Q5420758","display_name":"Expander code","level":5,"score":0.2946000099182129},{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.28519999980926514},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.28459998965263367},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.2806999981403351},{"id":"https://openalex.org/C2096984","wikidata":"https://www.wikidata.org/wiki/Q245464","display_name":"Cyclic code","level":5,"score":0.2800000011920929},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.266400009393692},{"id":"https://openalex.org/C206468330","wikidata":"https://www.wikidata.org/wiki/Q834373","display_name":"Code rate","level":3,"score":0.25540000200271606},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.2531000077724457},{"id":"https://openalex.org/C20079647","wikidata":"https://www.wikidata.org/wiki/Q1278039","display_name":"Prefix code","level":5,"score":0.2522999942302704}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tit.2017.2755682","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2755682","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:repositori.uji.es:10234/172910","is_oa":false,"landing_page_url":"http://hdl.handle.net/10234/172910","pdf_url":null,"source":{"id":"https://openalex.org/S4306400303","display_name":"Repositori UJI (Universitat Jaume I)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I10902133","host_organization_name":"Universitat Jaume I","host_organization_lineage":["https://openalex.org/I10902133"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:arXiv.org:1610.06363","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1610.06363","pdf_url":"https://arxiv.org/pdf/1610.06363","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:157.88.20.52:10324/31722","is_oa":true,"landing_page_url":"http://uvadoc.uva.es/handle/10324/31722","pdf_url":null,"source":{"id":"https://openalex.org/S4377196373","display_name":"UVaDOC Documentary Repository (University of Valladolid)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108103353","host_organization_name":"Universidad de Valladolid","host_organization_lineage":["https://openalex.org/I108103353"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.atira.dk:publications/47f54740-4dcd-4755-ade5-ba884f72e27e","is_oa":false,"landing_page_url":"https://vbn.aau.dk/da/publications/47f54740-4dcd-4755-ade5-ba884f72e27e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401731","display_name":"VBN Forskningsportal (Aalborg Universitet)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I891191580","host_organization_name":"Aalborg University","host_organization_lineage":["https://openalex.org/I891191580"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Galindo, C, Geil, H O, Hernando, F & Ruano Benito, D 2018, 'Improved constructions of nested code pairs', I E E E Transactions on Information Theory, vol. 64, no. 4, pp. 2444-2459. https://doi.org/10.1109/TIT.2017.2755682","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1610.06363","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1610.06363","pdf_url":"https://arxiv.org/pdf/1610.06363","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3143276367","display_name":null,"funder_award_id":"DFF-4002-00367","funder_id":"https://openalex.org/F4320310485","funder_display_name":"Natur og Univers, Det Frie Forskningsr\u00e5d"},{"id":"https://openalex.org/G854504215","display_name":null,"funder_award_id":"DFF-4002-00367","funder_id":"https://openalex.org/F4320322928","funder_display_name":"Danmarks Frie Forskningsfond"}],"funders":[{"id":"https://openalex.org/F4320310485","display_name":"Natur og Univers, Det Frie Forskningsr\u00e5d","ror":"https://ror.org/03ge1nb22"},{"id":"https://openalex.org/F4320322928","display_name":"Danmarks Frie Forskningsfond","ror":"https://ror.org/02sptwz63"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W284049292","https://openalex.org/W1534695542","https://openalex.org/W1903020140","https://openalex.org/W1977854174","https://openalex.org/W1980801869","https://openalex.org/W1984753322","https://openalex.org/W1998617809","https://openalex.org/W2003650502","https://openalex.org/W2017186546","https://openalex.org/W2019215605","https://openalex.org/W2022968516","https://openalex.org/W2029891988","https://openalex.org/W2047096647","https://openalex.org/W2047967498","https://openalex.org/W2051706912","https://openalex.org/W2060885602","https://openalex.org/W2063592138","https://openalex.org/W2068101455","https://openalex.org/W2075631080","https://openalex.org/W2078380442","https://openalex.org/W2091331782","https://openalex.org/W2093617931","https://openalex.org/W2097083932","https://openalex.org/W2099920789","https://openalex.org/W2109496295","https://openalex.org/W2111368253","https://openalex.org/W2113451741","https://openalex.org/W2114207424","https://openalex.org/W2115025292","https://openalex.org/W2123191702","https://openalex.org/W2128439756","https://openalex.org/W2130590206","https://openalex.org/W2133693898","https://openalex.org/W2135097120","https://openalex.org/W2136563111","https://openalex.org/W2141420453","https://openalex.org/W2143438504","https://openalex.org/W2145085841","https://openalex.org/W2152980678","https://openalex.org/W2157020220","https://openalex.org/W2162938940","https://openalex.org/W2167413626","https://openalex.org/W2172053063","https://openalex.org/W2539705156","https://openalex.org/W2581931326","https://openalex.org/W2963278054","https://openalex.org/W6681898972","https://openalex.org/W6732774480"],"related_works":[],"abstract_inverted_index":{"Two":[0],"new":[1,118],"constructions":[2,119],"of":[3,73,80,89,97,130],"linear":[4,99],"code":[5,83],"pairs":[6,88],"C":[7,12,36,54],"<sub":[8,13,28,32,37,43,47,55],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[9,14,29,33,38,44,48,51,56,59],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[10,39,49],"\u2282":[11],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[15,30,34,45,57],"are":[16,62,92],"given":[17],"for":[18,69,94],"which":[19],"the":[20,23,74,77,81,95,124],"codimension":[21],"and":[22,41,136],"relative":[24],"minimum":[25],"distances":[26],"M":[27,42],"(C":[31,46],",":[35,53],")":[40,61],"<sup":[50,58],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u22a5</sup>":[52,60],"good.":[63],"By":[64],"this,":[65],"we":[66],"mean":[67],"that":[68],"any":[70],"two":[71],"out":[72],"three":[75],"parameters":[76],"third":[78],"parameter":[79],"constructed":[82],"pair":[84],"is":[85],"large.":[86],"Such":[87],"nested":[90],"codes":[91,131],"indispensable":[93],"determination":[96],"good":[98],"ramp":[100],"secret":[101],"sharing":[102],"schemes.":[103],"They":[104],"can":[105],"also":[106],"be":[107],"used":[108],"to":[109,127],"ensure":[110],"reliable":[111],"communication":[112],"over":[113],"asymmetric":[114],"quantum":[115],"channels.":[116],"The":[117],"result":[120],"from":[121,133],"carefully":[122],"applying":[123],"Feng-Rao":[125],"bounds":[126],"a":[128],"family":[129],"defined":[132],"multivariate":[134],"polynomials":[135],"Cartesian":[137],"product":[138],"point":[139],"sets.":[140]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-10-28T00:00:00"}