{"id":"https://openalex.org/W2907006411","doi":"https://doi.org/10.1109/tit.2018.2840226","title":"Partial Permutation Decoding for Several Families of Linear and &lt;inline-formula&gt; &lt;tex-math notation=\"LaTeX\"&gt;${\\mathbb{Z}}_4$ &lt;/tex-math&gt; &lt;/inline-formula&gt;-Linear Codes","display_name":"Partial Permutation Decoding for Several Families of Linear and &lt;inline-formula&gt; &lt;tex-math notation=\"LaTeX\"&gt;${\\mathbb{Z}}_4$ &lt;/tex-math&gt; &lt;/inline-formula&gt;-Linear Codes","publication_year":2018,"publication_date":"2018-05-24","ids":{"openalex":"https://openalex.org/W2907006411","doi":"https://doi.org/10.1109/tit.2018.2840226","mag":"2907006411"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2018.2840226","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2840226","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/A5005890269","display_name":"Roland D. Barrolleta","orcid":"https://orcid.org/0000-0002-8792-2571"},"institutions":[{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Roland D. Barrolleta","raw_affiliation_strings":["Department of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Barcelona, Spain","Dept. of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Spain#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Barcelona, Spain","institution_ids":["https://openalex.org/I123044942"]},{"raw_affiliation_string":"Dept. of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Spain#TAB#","institution_ids":["https://openalex.org/I123044942"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080668151","display_name":"Merc\u00e8 Villanueva","orcid":"https://orcid.org/0000-0001-6179-0833"},"institutions":[{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Merce Villanueva","raw_affiliation_strings":["Department of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Barcelona, Spain","Dept. of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Spain#TAB#"],"raw_orcid":"https://orcid.org/0000-0001-6179-0833","affiliations":[{"raw_affiliation_string":"Department of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Barcelona, Spain","institution_ids":["https://openalex.org/I123044942"]},{"raw_affiliation_string":"Dept. of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Spain#TAB#","institution_ids":["https://openalex.org/I123044942"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5005890269"],"corresponding_institution_ids":["https://openalex.org/I123044942"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.15962417,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"65","issue":"1","first_page":"131","last_page":"141"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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":0.9979000091552734,"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":0.9929999709129333,"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/combinatorics","display_name":"Combinatorics","score":0.49387437105178833},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.46580296754837036},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.45257043838500977},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44578421115875244},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41882622241973877},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.4180510938167572},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3863322138786316},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.1559191346168518},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1074187159538269}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49387437105178833},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.46580296754837036},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.45257043838500977},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44578421115875244},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41882622241973877},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.4180510938167572},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3863322138786316},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.1559191346168518},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1074187159538269},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2018.2840226","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2840226","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":[{"id":"https://openalex.org/G6740744453","display_name":null,"funder_award_id":"TIN2016-77918-P (AEI/FEDER, UE)","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G877002546","display_name":null,"funder_award_id":"MTM2015-69138-REDT","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"}],"funders":[{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W647564967","https://openalex.org/W803102646","https://openalex.org/W1503013413","https://openalex.org/W1559343931","https://openalex.org/W1606480398","https://openalex.org/W1640881979","https://openalex.org/W1975177438","https://openalex.org/W1976677460","https://openalex.org/W1981297187","https://openalex.org/W1985683281","https://openalex.org/W1987011728","https://openalex.org/W1991819817","https://openalex.org/W1993416431","https://openalex.org/W1998728561","https://openalex.org/W2002792049","https://openalex.org/W2006920492","https://openalex.org/W2010825458","https://openalex.org/W2012943612","https://openalex.org/W2031230255","https://openalex.org/W2038681062","https://openalex.org/W2039133144","https://openalex.org/W2043253969","https://openalex.org/W2048870136","https://openalex.org/W2054296318","https://openalex.org/W2064375083","https://openalex.org/W2069145139","https://openalex.org/W2070442620","https://openalex.org/W2081939650","https://openalex.org/W2093434772","https://openalex.org/W2103398070","https://openalex.org/W2105694437","https://openalex.org/W2106513168","https://openalex.org/W2108211019","https://openalex.org/W2111162716","https://openalex.org/W2116119493","https://openalex.org/W2124775998","https://openalex.org/W2131418871","https://openalex.org/W2146361334","https://openalex.org/W2149814091","https://openalex.org/W2172854781","https://openalex.org/W2209705785","https://openalex.org/W2301865936","https://openalex.org/W2337803068","https://openalex.org/W2399318769","https://openalex.org/W2507710006","https://openalex.org/W2538118183","https://openalex.org/W2566000337","https://openalex.org/W2962972548","https://openalex.org/W2963573917","https://openalex.org/W3099018150","https://openalex.org/W3101163237","https://openalex.org/W4206775542","https://openalex.org/W4244691952","https://openalex.org/W4249397549","https://openalex.org/W4300529123","https://openalex.org/W6712466911"],"related_works":["https://openalex.org/W3203142394","https://openalex.org/W4302615923","https://openalex.org/W1974101135","https://openalex.org/W2351061015","https://openalex.org/W2017509870","https://openalex.org/W2990083380","https://openalex.org/W2964302506","https://openalex.org/W2989391174","https://openalex.org/W2579163092","https://openalex.org/W2028698464"],"abstract_inverted_index":{"A":[0],"general":[1],"criterion":[2],"to":[3,20,49],"obtain":[4],"s-PD-sets":[5,111],"of":[6,71,112,125,161],"minimum":[7],"size":[8,113],"s":[9,21,114,144,176],"+":[10,115],"1":[11,116,142,174],"for":[12,23,88,117,136,153,168],"partial":[13],"permutation":[14],"decoding,":[15],"which":[16,65],"enable":[17],"correction":[18],"up":[19],"errors,":[22],"systematic":[24],"codes":[25,37,52,64,80,103,124,160],"over":[26,53],"a":[27,72],"finite":[28],"field":[29],"Fq":[30],"and":[31,77,91,99,141,152,173],"Z":[32,59,118,154],"<sub":[33,55,60,119,155],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[34,56,61,120,129,133,148,156,165,180],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">4</sub>":[35,62,121,157],"-linear":[36,63,122,158],"is":[38],"provided.":[39,186],"We":[40],"show":[41],"how":[42],"this":[43,108],"technique":[44],"can":[45],"be":[46],"easily":[47],"applied":[48],"linear":[50,74,90],"cyclic":[51,75],"F":[54],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">q</sub>":[57],",":[58,135,167],"are":[66,104,184],"the":[67],"Gray":[68],"map":[69],"image":[70],"quaternary":[73],"code,":[76],"some":[78,89],"related":[79],"such":[81],"as":[82],"quasi-cyclic":[83],"codes.":[84],"Furthermore,":[85],"specific":[86],"results":[87],"nonlinear":[92],"binary":[93],"codes,":[94],"including":[95],"simplex,":[96],"Kerdock,":[97],"Delsarte-Goethals,":[98],"extended":[100],"dualized":[101],"Kerdock":[102],"given.":[105],"Finally,":[106],"applying":[107],"technique,":[109],"new":[110],"Hadamard":[123],"type":[126,162],"2":[127,146,172,178],"<sup":[128,132,147,164,179],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03b3</sup>":[130],"4":[131,140,163],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03b4</sup>":[134,149],"all":[137,169],"\u03b4":[138],"\u2265":[139,171],"<;":[143,145,175],"-":[150,182],"3;":[151],"simplex":[159],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">m</sup>":[166],"m":[170],"\u2264":[177],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">m+1</sup>":[181],"3,":[183],"also":[185]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
