{"id":"https://openalex.org/W4409475285","doi":"https://doi.org/10.1109/tit.2025.3561119","title":"Improved Bounds on the Size of Permutation Codes Under Kendall \u03c4 -Metric","display_name":"Improved Bounds on the Size of Permutation Codes Under Kendall \u03c4 -Metric","publication_year":2025,"publication_date":"2025-04-15","ids":{"openalex":"https://openalex.org/W4409475285","doi":"https://doi.org/10.1109/tit.2025.3561119"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2025.3561119","doi":"https://doi.org/10.1109/tit.2025.3561119","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3561119","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,"listed_in":["anvur-class-a","anvur-scientific","ccf-a","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"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"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2406.06029","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006066917","display_name":"Farzad Parvaresh","orcid":"https://orcid.org/0000-0001-5292-0915","observed_orcids":["https://orcid.org/0000-0001-5292-0915"]},"institutions":[{"id":"https://openalex.org/I39268498","display_name":"University of Isfahan","ror":"https://ror.org/05h9t7759","country_code":"IR","type":"education","lineage":["https://openalex.org/I39268498"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Farzad Parvaresh","raw_affiliation_strings":["Department of Electrical Engineering, Faculty of Engineering, University of Isfahan, Isfahan, Iran"],"raw_orcid":"https://orcid.org/0000-0001-5292-0915","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Faculty of Engineering, University of Isfahan, Isfahan, Iran","institution_ids":["https://openalex.org/I39268498"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074786582","display_name":"R. Sobhani","orcid":"https://orcid.org/0000-0001-6876-307X","observed_orcids":["https://orcid.org/0000-0001-6876-307X"]},"institutions":[{"id":"https://openalex.org/I39268498","display_name":"University of Isfahan","ror":"https://ror.org/05h9t7759","country_code":"IR","type":"education","lineage":["https://openalex.org/I39268498"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Reza Sobhani","raw_affiliation_strings":["Department of Applied Mathematics and Computer Science, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, Iran"],"raw_orcid":"https://orcid.org/0000-0001-6876-307X","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, Iran","institution_ids":["https://openalex.org/I39268498"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018447571","display_name":"Alir\u00e9za Abdollahi","orcid":"https://orcid.org/0000-0001-7277-4855","observed_orcids":["https://orcid.org/0000-0001-7277-4855"]},"institutions":[{"id":"https://openalex.org/I4210146419","display_name":"Institute for Research in Fundamental Sciences","ror":"https://ror.org/04xreqs31","country_code":"IR","type":"facility","lineage":["https://openalex.org/I4210146419"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Alireza Abdollahi","raw_affiliation_strings":["School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran"],"raw_orcid":"https://orcid.org/0000-0001-7277-4855","affiliations":[{"raw_affiliation_string":"School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran","institution_ids":["https://openalex.org/I4210146419"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041068888","display_name":"Javad Bagherian","orcid":"https://orcid.org/0009-0004-3321-6120","observed_orcids":["https://orcid.org/0009-0004-3321-6120"]},"institutions":[{"id":"https://openalex.org/I39268498","display_name":"University of Isfahan","ror":"https://ror.org/05h9t7759","country_code":"IR","type":"education","lineage":["https://openalex.org/I39268498"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Javad Bagherian","raw_affiliation_strings":["Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, Iran","institution_ids":["https://openalex.org/I39268498"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113359724","display_name":"Fatemeh Jafari","orcid":"https://orcid.org/0000-0001-7503-4289","observed_orcids":["https://orcid.org/0000-0001-7503-4289"]},"institutions":[{"id":"https://openalex.org/I39268498","display_name":"University of Isfahan","ror":"https://ror.org/05h9t7759","country_code":"IR","type":"education","lineage":["https://openalex.org/I39268498"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Fatemeh Jafari","raw_affiliation_strings":["Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, Iran"],"raw_orcid":"https://orcid.org/0000-0001-7503-4289","affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, Iran","institution_ids":["https://openalex.org/I39268498"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081307188","display_name":"Maryam Khatami","orcid":"https://orcid.org/0000-0002-4495-8507","observed_orcids":["https://orcid.org/0000-0002-4495-8507"]},"institutions":[{"id":"https://openalex.org/I39268498","display_name":"University of Isfahan","ror":"https://ror.org/05h9t7759","country_code":"IR","type":"education","lineage":["https://openalex.org/I39268498"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Maryam Khatami","raw_affiliation_strings":["Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, Iran"],"raw_orcid":"https://orcid.org/0000-0002-4495-8507","affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, Iran","institution_ids":["https://openalex.org/I39268498"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":1.2322,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.79387361,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"71","issue":"6","first_page":"4156","last_page":"4166"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9384999871253967,"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":0.9384999871253967,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.04610000178217888,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.004000000189989805,"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/permutation-codes","display_name":"permutation codes","score":0.9990000128746033},{"id":"https://openalex.org/keywords/rank-modulation","display_name":"rank modulation","score":0.8309999704360962},{"id":"https://openalex.org/keywords/code-size-bounds","display_name":"code size bounds","score":0.7770000100135803},{"id":"https://openalex.org/keywords/permutation-distance","display_name":"permutation distance","score":0.5299999713897705},{"id":"https://openalex.org/keywords/flash-memory","display_name":"flash memory","score":0.5690000057220459},{"id":"https://openalex.org/keywords/dna-sequencing","display_name":"DNA sequencing","score":0.6029999852180481},{"id":"https://openalex.org/keywords/shotgun-sequencing","display_name":"shotgun sequencing","score":0.8539999723434448}],"concepts":[{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6006159782409668},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.5663082599639893},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5598527193069458},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40497708320617676},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3856891691684723},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3813619911670685},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3677677512168884},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3236958980560303},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09182968735694885},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2025.3561119","doi":"https://doi.org/10.1109/tit.2025.3561119","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3561119","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,"listed_in":["anvur-class-a","anvur-scientific","ccf-a","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"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:2406.06029","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2406.06029","pdf_url":"https://arxiv.org/pdf/2406.06029","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2406.06029","doi":"https://doi.org/10.48550/arxiv.2406.06029","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2406.06029","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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:2406.06029","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2406.06029","pdf_url":"https://arxiv.org/pdf/2406.06029","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G400339533","display_name":null,"funder_award_id":"1401680050","funder_id":"https://openalex.org/F4320323627","funder_display_name":"School of Mathematics, Institute for Research in Fundamental Sciences"},{"id":"https://openalex.org/G5482153549","display_name":null,"funder_award_id":"4024979","funder_id":"https://openalex.org/F4320322243","funder_display_name":"Iran National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320322243","display_name":"Iran National Science Foundation","ror":"https://ror.org/03sr1ma14"},{"id":"https://openalex.org/F4320323627","display_name":"School of Mathematics, Institute for Research in Fundamental Sciences","ror":"https://ror.org/04xreqs31"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4409475285.pdf","grobid_xml":"https://content.openalex.org/works/W4409475285.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W2015751225","https://openalex.org/W2035122940","https://openalex.org/W2049706221","https://openalex.org/W2054557638","https://openalex.org/W2056018412","https://openalex.org/W2079920174","https://openalex.org/W2128970384","https://openalex.org/W2144030381","https://openalex.org/W2145923897","https://openalex.org/W2171980820","https://openalex.org/W2262696204","https://openalex.org/W2326500246","https://openalex.org/W2336019055","https://openalex.org/W2474954033","https://openalex.org/W2556566346","https://openalex.org/W2916828950","https://openalex.org/W3196492959","https://openalex.org/W4205833074","https://openalex.org/W4229706427","https://openalex.org/W4245156319","https://openalex.org/W4254448470","https://openalex.org/W4381615030","https://openalex.org/W4385627904","https://openalex.org/W4405954353"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2980963558","https://openalex.org/W2594778474","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W1976691234","https://openalex.org/W3212023493","https://openalex.org/W1922851888"],"abstract_inverted_index":{"In":[0,36,44,106],"order":[1],"to":[2,12,17],"overcome":[3],"the":[4,25,29,37,49,63,74,85,97,165],"challenges":[5],"caused":[6],"by":[7],"flash":[8],"memories":[9],"and":[10,92,100,120,137],"also":[11],"protect":[13],"against":[14],"errors":[15],"related":[16],"reading":[18],"information":[19],"stored":[20],"in":[21,24],"DNA":[22],"molecules":[23],"shotgun":[26],"sequencing":[27],"method,":[28],"rank":[30,38],"modulation":[31,39],"method":[32],"has":[33],"been":[34],"proposed.":[35],"framework,":[40],"codewords":[41],"are":[42],"permutations.":[43],"this":[45],"paper,":[46],"we":[47,95,108,129],"study":[48],"largest":[50],"size":[51],"P(n,":[52,104,111,142,169],"d)":[53,112],"of":[54,57,62,66,168],"permutation":[55],"codes":[56],"length":[58],"n,":[59],"i.e.,":[60],"subsets":[61],"set":[64],"Sn":[65],"all":[67,116,172],"permutations":[68],"on":[69],"{1,":[70,81],"...,":[71,82],"n}":[72],"with":[73],"minimum":[75],"distance":[76],"at":[77],"least":[78],"d":[79,124],"\u2208":[80],"(n/2)}":[83],"under":[84],"Kendall":[86],"\u03c4-metric.":[87],"By":[88],"presenting":[89],"an":[90],"algorithm":[91],"two":[93],"theorems,":[94],"improve":[96],"known":[98],"lower":[99],"upper":[101,166],"bounds":[102],"for":[103,115,132,171],"d).":[105],"particular,":[107],"show":[109],"that":[110,131],"=":[113],"4":[114],"n":[117,136,149,174],"\u2265":[118,175],"6":[119],"3/5":[121],"(n/2)":[122],"<":[123],"\u2264":[125,140,144],"2/3":[126],"(n/2).":[127],"Additionally,":[128],"prove":[130],"any":[133],"prime":[134],"number":[135],"integer":[138],"r":[139],"n/6,":[141],"3)":[143,170],"(n":[145],"\u2212":[146,148,150,152,157,159],"1)!":[147],"6r/\u221an2":[151],"8rn":[153],"+":[154],"20r2":[155],"\u221a(n":[156],"1)!/n(n":[158],"r)!.":[160],"This":[161],"result":[162],"greatly":[163],"improves":[164],"bound":[167],"primes":[173],"37.":[176]},"counts_by_year":[{"year":2025,"cited_by_count":3}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}
