{"id":"https://openalex.org/W1991706950","doi":"https://doi.org/10.1109/tit.2012.2193661","title":"On the Pseudocodeword Redundancy of Binary Linear Codes","display_name":"On the Pseudocodeword Redundancy of Binary Linear Codes","publication_year":2012,"publication_date":"2012-04-05","ids":{"openalex":"https://openalex.org/W1991706950","doi":"https://doi.org/10.1109/tit.2012.2193661","mag":"1991706950"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2012.2193661","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2193661","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/A5019886277","display_name":"Jens Zumbr\u00e4gel","orcid":null},"institutions":[{"id":"https://openalex.org/I100930933","display_name":"University College Dublin","ror":"https://ror.org/05m7pjf47","country_code":"IE","type":"education","lineage":["https://openalex.org/I100930933"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Jens Zumbragel","raw_affiliation_strings":["University College Dublin, Claude Shannon Institute, Belfield, Dublin 4, Ireland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University College Dublin, Claude Shannon Institute, Belfield, Dublin 4, Ireland","institution_ids":["https://openalex.org/I100930933"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048122752","display_name":"Vitaly Skachek","orcid":"https://orcid.org/0000-0002-0626-2437"},"institutions":[{"id":"https://openalex.org/I100930933","display_name":"University College Dublin","ror":"https://ror.org/05m7pjf47","country_code":"IE","type":"education","lineage":["https://openalex.org/I100930933"]},{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["IE","US"],"is_corresponding":false,"raw_author_name":"Vitaly Skachek","raw_affiliation_strings":["Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Montreal, Singapore","Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Singapore","University College Dublin, Claude Shannon Institute, Belfield, Dublin 4, Ireland","University of Illinois at Urbana-Champaign, Coordinated Science Laboratory, Urbana, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Montreal, Singapore","institution_ids":[]},{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Singapore","institution_ids":[]},{"raw_affiliation_string":"University College Dublin, Claude Shannon Institute, Belfield, Dublin 4, Ireland","institution_ids":["https://openalex.org/I100930933"]},{"raw_affiliation_string":"University of Illinois at Urbana-Champaign, Coordinated Science Laboratory, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014330907","display_name":"Mark F. Flanagan","orcid":"https://orcid.org/0000-0001-6552-7020"},"institutions":[{"id":"https://openalex.org/I100930933","display_name":"University College Dublin","ror":"https://ror.org/05m7pjf47","country_code":"IE","type":"education","lineage":["https://openalex.org/I100930933"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Mark F. Flanagan","raw_affiliation_strings":["University College Dublin, Claude Shannon Institute, Belfield, Dublin 4, Ireland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University College Dublin, Claude Shannon Institute, Belfield, Dublin 4, Ireland","institution_ids":["https://openalex.org/I100930933"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3537,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.92360352,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"58","issue":"7","first_page":"4848","last_page":"4861"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":1.0,"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"}},{"id":"https://openalex.org/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9995999932289124,"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/T11130","display_name":"Coding theory and cryptography","score":0.9990000128746033,"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/hamming-code","display_name":"Hamming code","score":0.7203959226608276},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.6675922274589539},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6613812446594238},{"id":"https://openalex.org/keywords/redundancy","display_name":"Redundancy (engineering)","score":0.5470545887947083},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.5087016224861145},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48896706104278564},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4853576719760895},{"id":"https://openalex.org/keywords/parity-check-matrix","display_name":"Parity-check matrix","score":0.4767009913921356},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.46081772446632385},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.43357110023498535},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4311942458152771},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.42665421962738037},{"id":"https://openalex.org/keywords/hamming","display_name":"Hamming(7,4)","score":0.4105024039745331},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.4041723310947418},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40070196986198425},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2210114598274231},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.18870168924331665}],"concepts":[{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.7203959226608276},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.6675922274589539},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6613812446594238},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.5470545887947083},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.5087016224861145},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48896706104278564},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4853576719760895},{"id":"https://openalex.org/C95925971","wikidata":"https://www.wikidata.org/wiki/Q3100414","display_name":"Parity-check matrix","level":4,"score":0.4767009913921356},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.46081772446632385},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.43357110023498535},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4311942458152771},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.42665421962738037},{"id":"https://openalex.org/C112932734","wikidata":"https://www.wikidata.org/wiki/Q2322550","display_name":"Hamming(7,4)","level":5,"score":0.4105024039745331},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.4041723310947418},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40070196986198425},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2210114598274231},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.18870168924331665},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2012.2193661","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2193661","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:CiteSeerX.psu:10.1.1.770.1998","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.770.1998","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1103.3641.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W7241855","https://openalex.org/W1484692004","https://openalex.org/W1538894044","https://openalex.org/W1588943481","https://openalex.org/W1595640491","https://openalex.org/W1606480398","https://openalex.org/W2033546746","https://openalex.org/W2035309551","https://openalex.org/W2101011172","https://openalex.org/W2104459449","https://openalex.org/W2112682069","https://openalex.org/W2113672208","https://openalex.org/W2114869758","https://openalex.org/W2115769160","https://openalex.org/W2119990840","https://openalex.org/W2133945375","https://openalex.org/W2135573812","https://openalex.org/W2140227657","https://openalex.org/W2142414818","https://openalex.org/W2154287427","https://openalex.org/W2169134868","https://openalex.org/W2172151521","https://openalex.org/W2532468848","https://openalex.org/W2895239415","https://openalex.org/W4285719527","https://openalex.org/W6628810906","https://openalex.org/W6632091454","https://openalex.org/W6635539370"],"related_works":["https://openalex.org/W2008960744","https://openalex.org/W2740543340","https://openalex.org/W2105471374","https://openalex.org/W2158117886","https://openalex.org/W2371167013","https://openalex.org/W1987803429","https://openalex.org/W2963549154","https://openalex.org/W1581584131","https://openalex.org/W2164611661","https://openalex.org/W2125814644"],"abstract_inverted_index":{"For":[0],"a":[1,35,63],"binary":[2,18],"linear":[3],"code,":[4],"the":[5,11,17,22,29,40,47,52,71,106,118],"pseudocodeword":[6,65,72,87],"redundancy":[7,73],"with":[8],"respect":[9],"to":[10,27,46],"additive":[12],"white":[13],"Gaussian":[14],"noise":[15],"channel,":[16,20],"symmetric":[19],"or":[21],"max-fractional":[23],"weight":[24],"is":[25,44,55,125],"defined":[26],"be":[28],"smallest":[30],"number":[31],"of":[32,51,77,92,108,111,121],"rows":[33],"in":[34],"parity-check":[36],"matrix":[37],"such":[38],"that":[39,57],"corresponding":[41],"minimum":[42,48],"pseudoweight":[43],"equal":[45],"Hamming":[49],"distance":[50],"code.":[53],"It":[54],"shown":[56],"most":[58,96,114],"codes":[59,80,91,110],"do":[60],"not":[61],"have":[62],"finite":[64],"redundancy.":[66],"Also,":[67],"upper":[68],"bounds":[69],"on":[70,82,105],"for":[74,89,116],"some":[75],"families":[76],"codes,":[78],"including":[79],"based":[81],"designs,":[83],"are":[84,98,103],"provided.":[85],"The":[86],"redundancies":[88],"all":[90],"small":[93],"length":[94,112],"(at":[95],"9)":[97],"computed.":[99],"Furthermore,":[100],"comprehensive":[101],"results":[102],"provided":[104],"cases":[107],"cyclic":[109],"at":[113],"250":[115],"which":[117],"eigenvalue":[119],"bound":[120],"Vontobel":[122],"and":[123],"Koetter":[124],"sharp.":[126]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}