{"id":"https://openalex.org/W1963871092","doi":"https://doi.org/10.1137/s0097539797323571","title":"The Parametrized Complexity of Some Fundamental Problems in Coding Theory","display_name":"The Parametrized Complexity of Some Fundamental Problems in Coding Theory","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W1963871092","doi":"https://doi.org/10.1137/s0097539797323571","mag":"1963871092"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539797323571","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539797323571","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5110868906","display_name":"Rod Downey","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rod G. Downey","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054676766","display_name":"Michael R. Fellows","orcid":"https://orcid.org/0000-0002-6148-9212"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael R. Fellows","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004102644","display_name":"Alexander Vardy","orcid":"https://orcid.org/0000-0003-3303-9078"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexander Vardy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5019046311","display_name":"Geoff Whittle","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Geoff Whittle","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5158,"has_fulltext":false,"cited_by_count":77,"citation_normalized_percentile":{"value":0.73665634,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"29","issue":"2","first_page":"545","last_page":"570"},"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":0.9998000264167786,"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":0.9997000098228455,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7522143721580505},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.60903400182724},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5659016370773315},{"id":"https://openalex.org/keywords/coding-theory","display_name":"Coding theory","score":0.52869713306427},{"id":"https://openalex.org/keywords/lattice-problem","display_name":"Lattice problem","score":0.5042153596878052},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.4687892198562622},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.42470628023147583},{"id":"https://openalex.org/keywords/list-decoding","display_name":"List decoding","score":0.4218846559524536},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.24893301725387573},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.23310843110084534},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1805151402950287},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.16952279210090637}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7522143721580505},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.60903400182724},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5659016370773315},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.52869713306427},{"id":"https://openalex.org/C168482242","wikidata":"https://www.wikidata.org/wiki/Q6497128","display_name":"Lattice problem","level":3,"score":0.5042153596878052},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.4687892198562622},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.42470628023147583},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.4218846559524536},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.24893301725387573},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.23310843110084534},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1805151402950287},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.16952279210090637}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0097539797323571","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539797323571","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W139921209","https://openalex.org/W1497155250","https://openalex.org/W1505918075","https://openalex.org/W1972577597","https://openalex.org/W1982384331","https://openalex.org/W1997639167","https://openalex.org/W2011039300","https://openalex.org/W2022841964","https://openalex.org/W2029604753","https://openalex.org/W2035929826","https://openalex.org/W2055423880","https://openalex.org/W2061513598","https://openalex.org/W2064252342","https://openalex.org/W2075503802","https://openalex.org/W2095761422","https://openalex.org/W2111319461","https://openalex.org/W2112313560","https://openalex.org/W2115667895","https://openalex.org/W2122406806","https://openalex.org/W2133068391","https://openalex.org/W2144050783","https://openalex.org/W2171712712","https://openalex.org/W2293231900","https://openalex.org/W2745281314","https://openalex.org/W3144422206"],"related_works":["https://openalex.org/W3017203753","https://openalex.org/W3083229674","https://openalex.org/W4205451769","https://openalex.org/W2385322349","https://openalex.org/W3096151594","https://openalex.org/W2369600518","https://openalex.org/W2964031101","https://openalex.org/W2983681086","https://openalex.org/W4200209838","https://openalex.org/W2126877780"],"abstract_inverted_index":{"The":[0,40],"parametrized":[1,36],"complexity":[2,37],"of":[3,6,12,42,59,71,90,114,125,140,185],"a":[4,60,78,123,128,135],"number":[5],"fundamental":[7],"problems":[8,45,181,197,200],"in":[9,54,85,201],"the":[10,22,35,66,110,148,169,183],"theory":[11],"linear":[13,104],"codes":[14],"and":[15,29,51,127,156,188,198],"integer":[16,118,130,174],"lattices":[17,175],"is":[18,75,93,97,134,154,160,176],"explored.":[19],"Concerning":[20,106],"codes,":[21],"main":[23],"results":[24,92],"are":[25,32,182,203],"that":[26,94,151,158,168],"MAXIMUM-LIKELIHOOD":[27,189],"DECODING":[28,190],"WEIGHT":[30,186],"DISTRUBUTION":[31,187],"hard":[33,101,162,177],"for":[34,73,102,116,147,163,173,178,191],"class":[38],"W[1].":[39,164,179],"NP-completeness":[41],"these":[43,196],"two":[44],"was":[46],"established":[47],"by":[48,57,122],"Berlekamp,":[49],"McEliece,":[50],"van":[52],"Tilborg":[53],"1978":[55],"using":[56],"means":[58],"reduction":[61],"from":[62,82],"THREE-DIMENSIONAL":[63],"MATCHING.":[64],"On":[65],"other":[67],"hand,":[68],"our":[69,91],"proof":[70],"hardness":[72],"W[1]":[74],"based":[76],"on":[77],"parametric":[79],"polynomial-time":[80],"transformation":[81],"PERFECT":[83],"CODE":[84],"graphs.":[86],"An":[87],"immediate":[88],"consequence":[89],"bounded-distance":[95],"decoding":[96],"likely":[98],"to":[99],"be":[100],"binary":[103],"codes.":[105],"lattices,":[107],"we":[108,166],"address":[109],"THETA":[111,152],"SERIES":[112,153],"problem":[113,172],"determining":[115],"an":[117],"lattice":[119],"$\\L$":[120],"%given":[121],"set":[124],"generators,":[126],"positive":[129],"k":[131],"whether":[132],"there":[133],"vector":[136],"$x":[137],"\\in":[138],"\\L$":[139],"Euclidean":[141],"norm":[142],"k.":[143],"We":[144],"prove":[145,167],"here":[146],"first":[149],"time":[150],"NP-complete":[155],"show":[157],"it":[159],"also":[161],"Furthermore,":[165],"NEAREST":[170],"VECTOR":[171],"These":[180],"counterparts":[184],"lattices.":[192],"Relations":[193],"between":[194],"all":[195],"combinatorial":[199],"graphs":[202],"discussed.":[204]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}