{"id":"https://openalex.org/W2043280803","doi":"https://doi.org/10.1109/tit.2014.2331677","title":"Pseudocodewords of Parity-Check Codes Over Fields of Prime Cardinality","display_name":"Pseudocodewords of Parity-Check Codes Over Fields of Prime Cardinality","publication_year":2014,"publication_date":"2014-06-23","ids":{"openalex":"https://openalex.org/W2043280803","doi":"https://doi.org/10.1109/tit.2014.2331677","mag":"2043280803"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2014.2331677","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2331677","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/A5001009310","display_name":"Wittawat Kositwattanarerk","orcid":null},"institutions":[{"id":"https://openalex.org/I25399158","display_name":"Mahidol University","ror":"https://ror.org/01znkr924","country_code":"TH","type":"education","lineage":["https://openalex.org/I25399158"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Wittawat Kositwattanarerk","raw_affiliation_strings":["Department of Mathematics, Mahidol University, Bangkok, Thailand","Dept. of Math., Mahidol Univ., Bangkok, Thailand"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Mahidol University, Bangkok, Thailand","institution_ids":["https://openalex.org/I25399158"]},{"raw_affiliation_string":"Dept. of Math., Mahidol Univ., Bangkok, Thailand","institution_ids":["https://openalex.org/I25399158"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084201022","display_name":"Gretchen L. Matthews","orcid":"https://orcid.org/0000-0002-8977-8171"},"institutions":[{"id":"https://openalex.org/I8078737","display_name":"Clemson University","ror":"https://ror.org/037s24f05","country_code":"US","type":"education","lineage":["https://openalex.org/I8078737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gretchen L. Matthews","raw_affiliation_strings":["Department of Mathematical Sciences, Clemson University, Clemson, SC, USA","Dept. of Math. Sci., Clemson Univ., Clemson, SC, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Clemson University, Clemson, SC, USA","institution_ids":["https://openalex.org/I8078737"]},{"raw_affiliation_string":"Dept. of Math. Sci., Clemson Univ., Clemson, SC, USA#TAB#","institution_ids":["https://openalex.org/I8078737"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001009310"],"corresponding_institution_ids":["https://openalex.org/I25399158"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12940891,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"60","issue":"9","first_page":"5215","last_page":"5227"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9997000098228455,"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":0.9997000098228455,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9988999962806702,"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/T12029","display_name":"DNA and Biological Computing","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.671154260635376},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5877445936203003},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.5226383209228516},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5191265940666199},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5072019100189209},{"id":"https://openalex.org/keywords/parity-check-matrix","display_name":"Parity-check matrix","score":0.49560439586639404},{"id":"https://openalex.org/keywords/code-word","display_name":"Code word","score":0.3418150544166565},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29389387369155884},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22968381643295288}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.671154260635376},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5877445936203003},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.5226383209228516},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5191265940666199},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5072019100189209},{"id":"https://openalex.org/C95925971","wikidata":"https://www.wikidata.org/wiki/Q3100414","display_name":"Parity-check matrix","level":4,"score":0.49560439586639404},{"id":"https://openalex.org/C153207627","wikidata":"https://www.wikidata.org/wiki/Q863873","display_name":"Code word","level":3,"score":0.3418150544166565},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29389387369155884},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22968381643295288},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2014.2331677","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2331677","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":[{"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education","score":0.47999998927116394}],"awards":[{"id":"https://openalex.org/G6661078613","display_name":null,"funder_award_id":"H-98230-06-1-0008","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"}],"funders":[{"id":"https://openalex.org/F4320311089","display_name":"National Security Agency","ror":"https://ror.org/0047bvr32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W7241855","https://openalex.org/W1526262508","https://openalex.org/W1538894044","https://openalex.org/W1652876111","https://openalex.org/W1981173846","https://openalex.org/W1988024462","https://openalex.org/W2021644092","https://openalex.org/W2033546746","https://openalex.org/W2035309551","https://openalex.org/W2038115820","https://openalex.org/W2060677426","https://openalex.org/W2062908445","https://openalex.org/W2065212815","https://openalex.org/W2103604544","https://openalex.org/W2114811284","https://openalex.org/W2116815462","https://openalex.org/W2126256086","https://openalex.org/W2134500865","https://openalex.org/W2137813581","https://openalex.org/W2167734735","https://openalex.org/W2169134868","https://openalex.org/W2170862479","https://openalex.org/W2173776306","https://openalex.org/W2532468848","https://openalex.org/W3102546565","https://openalex.org/W3103990458","https://openalex.org/W4302194958","https://openalex.org/W6600302457","https://openalex.org/W6632091454","https://openalex.org/W6658471458","https://openalex.org/W6764775184"],"related_works":["https://openalex.org/W2361015587","https://openalex.org/W2121408388","https://openalex.org/W2090054304","https://openalex.org/W2508865029","https://openalex.org/W90969106","https://openalex.org/W98604564","https://openalex.org/W2171839442","https://openalex.org/W2358182703","https://openalex.org/W2145403642","https://openalex.org/W2113526583"],"abstract_inverted_index":{"This":[0,181],"paper":[1],"considers":[2],"pseudocodewords":[3,35,52,79,106,156,189,214],"of":[4,57,74,103,107,118,131,173,190,215],"lowdensity":[5],"parity-check":[6,175],"codes":[7,46,108,191,216],"over":[8,16,47,109,145,192,208,217],"alphabets":[9],"with":[10,155],"prime":[11,119],"cardinality":[12,120],"p":[13],"for":[14,188,206,228],"use":[15],"the":[17,48,58,66,71,75,78,86,115,164,174,229],"p-ary":[18],"symmetric":[19],"channel.":[20],"Pseudocodewords":[21],"are":[22,80,157,169,222],"decoding":[23,40],"algorithm":[24],"outputs":[25],"that":[26,89,105],"may":[27],"not":[28],"be":[29,63],"legitimate":[30],"codewords.":[31],"Here,":[32],"we":[33,99,127],"consider":[34],"arising":[36],"from":[37],"graph":[38],"cover":[39],"and":[41,134,178,185,197,202],"linear":[42],"programming":[43],"decoding.":[44],"For":[45],"binary":[49],"alphabet,":[50],"such":[51],"correspond":[53],"to":[54,93,142,159],"rational":[55],"points":[56],"fundamental":[59,67,76,87,231],"polytope.":[60],"They":[61],"can":[62],"characterized":[64],"via":[65],"cone,":[68],"which":[69,137],"is":[70],"conic":[72],"hull":[73],"polytope;":[77],"precisely":[81],"those":[82,207],"integer":[83],"vectors":[84],"within":[85],"cone":[88],"reduce":[90],"modulo":[91],"2":[92],"a":[94,101,129,135,139,183,203,225],"codeword.":[95],"In":[96,211],"this":[97],"paper,":[98],"determine":[100],"set":[102],"conditions":[104],"F":[110,146,193,198,218],"<sub":[111,147,194,199,219],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[112,148,195,200,220],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">p</sub>":[113,149],",":[114],"finite":[116],"field":[117],"p,":[121],"must":[122],"satisfy.":[123],"To":[124],"do":[125],"so,":[126],"introduce":[128],"class":[130],"critical":[132,165,179],"multisets":[133],"mapping,":[136],"associates":[138],"real":[140,152],"number":[141],"each":[143],"pseudocodeword":[144],".":[150],"The":[151,167],"numbers":[153],"associated":[154],"subject":[158],"lower":[160],"bounds":[161],"imposed":[162],"by":[163],"multisets.":[166,180],"inequalities":[168],"given":[170],"in":[171],"terms":[172],"matrix":[176],"entries":[177],"gives":[182],"necessary":[184,204],"sufficient":[186],"condition":[187,205],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[196],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">3</sub>":[201,221],"larger":[209],"alphabets.":[210],"addition,":[212],"irreducible":[213],"found":[223],"as":[224],"Hilbert":[226],"basis":[227],"lifted":[230],"cone.":[232]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}