{"id":"https://openalex.org/W2152423532","doi":"https://doi.org/10.1109/tit.2011.2162185","title":"Involutions in Binary Perfect Codes","display_name":"Involutions in Binary Perfect Codes","publication_year":2011,"publication_date":"2011-09-01","ids":{"openalex":"https://openalex.org/W2152423532","doi":"https://doi.org/10.1109/tit.2011.2162185","mag":"2152423532"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2011.2162185","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2162185","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/A5065292754","display_name":"Cristina Fern\u00e1ndez-C\u00f3rdoba","orcid":"https://orcid.org/0000-0001-5880-144X"},"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":"Cristina Fernandez-Cordoba","raw_affiliation_strings":["Department of Information and Communications Engineering, Universitat Aut\u00f2noma Barcelona, Bellaterra, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information and Communications Engineering, Universitat Aut\u00f2noma Barcelona, Bellaterra, Spain","institution_ids":["https://openalex.org/I123044942"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069038206","display_name":"Kevin T. Phelps","orcid":null},"institutions":[{"id":"https://openalex.org/I82497590","display_name":"Auburn University","ror":"https://ror.org/02v80fc35","country_code":"US","type":"education","lineage":["https://openalex.org/I82497590"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kevin T. Phelps","raw_affiliation_strings":["Mathematics and Statistics Department, Aubum University, Auburn, AL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics and Statistics Department, Aubum University, Auburn, AL, USA","institution_ids":["https://openalex.org/I82497590"]}]},{"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":"Merc\u00e8 Villanueva","raw_affiliation_strings":["Department of Information and Communications Engineering, Universitat Aut\u00f2noma Barcelona, Bellaterra, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information and Communications Engineering, Universitat Aut\u00f2noma Barcelona, Bellaterra, Spain","institution_ids":["https://openalex.org/I123044942"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1982,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.89632035,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"57","issue":"9","first_page":"5926","last_page":"5932"},"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":0.9865999817848206,"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/T10849","display_name":"Finite Group Theory Research","score":0.9865000247955322,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3188837766647339}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3188837766647339}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2011.2162185","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2162185","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1519204501","https://openalex.org/W1606480398","https://openalex.org/W1964584687","https://openalex.org/W1992596326","https://openalex.org/W1998811014","https://openalex.org/W2005311334","https://openalex.org/W2006247496","https://openalex.org/W2010238614","https://openalex.org/W2045545810","https://openalex.org/W2084697491","https://openalex.org/W2093292941","https://openalex.org/W2116611140","https://openalex.org/W2118297173","https://openalex.org/W2121857821","https://openalex.org/W2150911857","https://openalex.org/W2155439537","https://openalex.org/W2160658340","https://openalex.org/W2166966427","https://openalex.org/W2487426028","https://openalex.org/W3099682685"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2530322880","https://openalex.org/W1596801655","https://openalex.org/W2359140296"],"abstract_inverted_index":{"Given":[0],"a":[1,41],"1-perfect":[2,96,145,207],"code":[3],"<i":[4,13,17,21,26,31,35,49,66,70,75,79,90,107,120,128,136,140,149,153,164,170,180,187,191,198,202,211,215,221,225,229,238,250,257,261,266,271],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[5,14,18,22,27,32,36,50,67,71,76,80,91,108,121,129,137,141,150,154,165,171,181,188,192,199,203,212,216,222,226,230,239,251,258,262,267,272],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">C</i>":[6,15,23,33,37,51,72,81],",":[7,16,39],"the":[8,44,84,98,101],"group":[9,45],"of":[10,12,43,46,48,60,86,103,147,209],"symmetries":[11,59],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Sym</i>":[19,77],"(":[20,69,78],")={\u03c0":[24],"\u2208":[25],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Sn</i>":[28],"|":[29,106,110,163,167],"\u03c0(":[30],")=":[34],"}":[38],"is":[40,255],"subgroup":[42],"automorphisms":[47],".":[52],"In":[53],"this":[54],"paper,":[55],"we":[56],"focus":[57],"on":[58],"order":[61],"two,":[62],"i.e.,":[63],"involutions.":[64],"Let":[65],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">InvF</i>":[68],")":[73,82],"\u2286":[74],"be":[83],"set":[85],"involutions":[87],"that":[88,161,235],"stabilize":[89],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">F</i>":[92,109,166],"pointwise.":[93],"For":[94,118],"linear":[95,144],"codes,":[97],"possibilities":[99],"for":[100,178],"number":[102],"fixed":[104],"points":[105],"are":[111,175,243],"given,":[112],"establishing":[113],"lower":[114],"and":[115,125,195,232,265],"upper":[116],"bounds.":[117],"any":[119,126,179],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">m</i>":[122,142,155,182,193,204,217,227,252,263,273],"\u2265":[123,183,253],"2":[124,169,237],"value":[127],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k</i>":[130,138,172,200,240,268],"between":[131],"these":[132],"bounds,":[133],"[m/2]":[134,196],"\u2264":[135,139,186,190,197,201],"-1,":[143,194,205],"codes":[146,208],"length":[148,210],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</i>":[151,213,223],"=2":[152,214],"-1":[156,173,218,241,264],"which":[157],"have":[158],"an":[159,233],"involution":[160,234],"fixes":[162,236],"=":[168,260,269],"coordinates":[174,242],"constructed.":[176],"Moreover,":[177],"4,":[184],"1":[185],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">r</i>":[189,231,259],"nonlinear":[206],"having":[219],"rank":[220],"-":[224],"+":[228],"also":[244],"constructed,":[245],"except":[246],"one":[247],"case,":[248],"when":[249],"6":[254],"even,":[256],"[":[270],"/2].":[274]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
