{"id":"https://openalex.org/W2914227629","doi":"https://doi.org/10.1109/tit.2019.2957354","title":"New Lower Bounds for Permutation Codes Using Linear Block Codes","display_name":"New Lower Bounds for Permutation Codes Using Linear Block Codes","publication_year":2019,"publication_date":"2019-12-03","ids":{"openalex":"https://openalex.org/W2914227629","doi":"https://doi.org/10.1109/tit.2019.2957354","mag":"2914227629"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2019.2957354","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2019.2957354","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1901.08858","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050777736","display_name":"Giacomo Micheli","orcid":"https://orcid.org/0000-0002-5265-5207"},"institutions":[{"id":"https://openalex.org/I2613432","display_name":"University of South Florida","ror":"https://ror.org/032db5x82","country_code":"US","type":"education","lineage":["https://openalex.org/I2613432"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Giacomo Micheli","raw_affiliation_strings":["Department of Mathematics, University of South Florida, Tampa, USA","[Department of Mathematics, University of South Florida, Tampa, FL, USA]"],"raw_orcid":"https://orcid.org/0000-0002-5265-5207","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of South Florida, Tampa, USA","institution_ids":["https://openalex.org/I2613432"]},{"raw_affiliation_string":"[Department of Mathematics, University of South Florida, Tampa, FL, USA]","institution_ids":["https://openalex.org/I2613432"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085377486","display_name":"Alessandro Neri","orcid":"https://orcid.org/0000-0002-2020-1040"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210126360","display_name":"Centre Inria de Saclay","ror":"https://ror.org/0315e5x55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210126360"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alessandro Neri","raw_affiliation_strings":["INRIA Saclay \u00cele-de-France, Palaiseau, France","Inria Saclay Ile-de-France, Palaiseau, France#TAB#"],"raw_orcid":"https://orcid.org/0000-0002-2020-1040","affiliations":[{"raw_affiliation_string":"INRIA Saclay \u00cele-de-France, Palaiseau, France","institution_ids":["https://openalex.org/I4210126360","https://openalex.org/I1326498283"]},{"raw_affiliation_string":"Inria Saclay Ile-de-France, Palaiseau, France#TAB#","institution_ids":["https://openalex.org/I4210126360"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01360638,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"66","issue":"7","first_page":"4019","last_page":"4025"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9998999834060669,"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/T10796","display_name":"Cooperative Communication and Network Coding","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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6912276744842529},{"id":"https://openalex.org/keywords/permutation-matrix","display_name":"Permutation matrix","score":0.6823877096176147},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6444766521453857},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.625196099281311},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.5879625082015991},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5393204092979431},{"id":"https://openalex.org/keywords/bit-reversal-permutation","display_name":"Bit-reversal permutation","score":0.5261715650558472},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.50283282995224},{"id":"https://openalex.org/keywords/partial-permutation","display_name":"Partial permutation","score":0.5007174015045166},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.4961777627468109},{"id":"https://openalex.org/keywords/permutation-graph","display_name":"Permutation graph","score":0.47683730721473694},{"id":"https://openalex.org/keywords/cyclic-permutation","display_name":"Cyclic permutation","score":0.4595254063606262},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2203230857849121},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1822880208492279},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.16091805696487427},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.10632485151290894},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.06390082836151123},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.047426313161849976}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6912276744842529},{"id":"https://openalex.org/C84140500","wikidata":"https://www.wikidata.org/wiki/Q851512","display_name":"Permutation matrix","level":3,"score":0.6823877096176147},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6444766521453857},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.625196099281311},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.5879625082015991},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5393204092979431},{"id":"https://openalex.org/C175473596","wikidata":"https://www.wikidata.org/wiki/Q4918660","display_name":"Bit-reversal permutation","level":4,"score":0.5261715650558472},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.50283282995224},{"id":"https://openalex.org/C145633696","wikidata":"https://www.wikidata.org/wiki/Q1401935","display_name":"Partial permutation","level":4,"score":0.5007174015045166},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.4961777627468109},{"id":"https://openalex.org/C68965932","wikidata":"https://www.wikidata.org/wiki/Q7169369","display_name":"Permutation graph","level":3,"score":0.47683730721473694},{"id":"https://openalex.org/C77670614","wikidata":"https://www.wikidata.org/wiki/Q212130","display_name":"Cyclic permutation","level":3,"score":0.4595254063606262},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2203230857849121},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1822880208492279},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.16091805696487427},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.10632485151290894},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.06390082836151123},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.047426313161849976},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2019.2957354","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2019.2957354","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:arXiv.org:1901.08858","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1901.08858","pdf_url":"https://arxiv.org/pdf/1901.08858","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":"","raw_type":"text"},{"id":"mag:2914227629","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1901.08858","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1901.08858","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1901.08858","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1901.08858","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1901.08858","pdf_url":"https://arxiv.org/pdf/1901.08858","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4446820173","display_name":"Algebraic Methods for Rank-Metric Codes in Post-Quantum Cryptography and Communications","funder_award_id":"187711","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5226484893","display_name":"Algebraic Constructions and Decodingof Rank Metric Codes with Applications to Network Coding and Code based Cryptography","funder_award_id":"169510","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G7200658341","display_name":"Regular Sets of Irreducible Polynomials, Applications of a Local to Global Principle for densities, and Cryptography","funder_award_id":"171249","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2914227629.pdf","grobid_xml":"https://content.openalex.org/works/W2914227629.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1519782116","https://openalex.org/W1530125006","https://openalex.org/W1606480398","https://openalex.org/W1972398039","https://openalex.org/W1974009707","https://openalex.org/W1974627484","https://openalex.org/W2012785774","https://openalex.org/W2018972846","https://openalex.org/W2040651417","https://openalex.org/W2041807026","https://openalex.org/W2050687505","https://openalex.org/W2063121374","https://openalex.org/W2066218472","https://openalex.org/W2069390698","https://openalex.org/W2080132708","https://openalex.org/W2104251118","https://openalex.org/W2113142402","https://openalex.org/W2131029388","https://openalex.org/W2147353956","https://openalex.org/W2148602768","https://openalex.org/W2199172791","https://openalex.org/W2475905526","https://openalex.org/W2556566346","https://openalex.org/W2963221477","https://openalex.org/W3101884795","https://openalex.org/W3144798926","https://openalex.org/W4239704585","https://openalex.org/W4247901601"],"related_works":["https://openalex.org/W2951538996","https://openalex.org/W2125494331","https://openalex.org/W2073788610","https://openalex.org/W1792388367","https://openalex.org/W2150830501","https://openalex.org/W2171294544","https://openalex.org/W2125774675","https://openalex.org/W1543977106","https://openalex.org/W2018972846","https://openalex.org/W3160733293","https://openalex.org/W2136137499","https://openalex.org/W2169117254","https://openalex.org/W2743327613","https://openalex.org/W2606317739","https://openalex.org/W2000812559","https://openalex.org/W3136820369","https://openalex.org/W2128970384","https://openalex.org/W2155925529","https://openalex.org/W2015848652","https://openalex.org/W2024722282"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,48,78],"prove":[4,52],"new":[5,80],"lower":[6,81],"bounds":[7,82],"for":[8,83],"the":[9,17,23,32,53,60,88,91,105],"maximal":[10],"size":[11],"of":[12,19,25,34,39,55,63,100,104],"permutation":[13,20,57,84,106],"codes":[14,21,85],"by":[15],"connecting":[16],"theory":[18,24],"with":[22],"linear":[26,45],"block":[27,46],"codes.":[28],"More":[29],"specifically,":[30],"using":[31],"columns":[33],"a":[35,56],"parity":[36],"check":[37],"matrix":[38],"an":[40],"[n,k,d]":[41],"<sub":[42],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[43],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">q</sub>":[44],"code,":[47],"are":[49],"able":[50],"to":[51],"existence":[54],"code":[58],"in":[59,90,97],"symmetric":[61],"group":[62],"degree":[64],"n,":[65],"having":[66],"minimum":[67],"distance":[68,103],"at":[69],"least":[70],"d":[71],"and":[72,93,102],"large":[73],"cardinality.":[74],"With":[75],"our":[76],"technique,":[77],"obtain":[79],"that":[86],"enhance":[87],"ones":[89],"literature":[92],"provide":[94],"asymptotic":[95],"improvements":[96],"certain":[98],"regimes":[99],"length":[101],"code.":[107]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}