{"id":"https://openalex.org/W2136524203","doi":"https://doi.org/10.1109/tit.2008.2011439","title":"Computing Partial Walsh Transform From the Algebraic Normal Form of a Boolean Function","display_name":"Computing Partial Walsh Transform From the Algebraic Normal Form of a Boolean Function","publication_year":2009,"publication_date":"2009-02-26","ids":{"openalex":"https://openalex.org/W2136524203","doi":"https://doi.org/10.1109/tit.2008.2011439","mag":"2136524203"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2008.2011439","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2008.2011439","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/A5102051987","display_name":"Kishan Chand Gupta","orcid":null},"institutions":[{"id":"https://openalex.org/I6498739","display_name":"Indian Statistical Institute","ror":"https://ror.org/00q2w1j53","country_code":"IN","type":"education","lineage":["https://openalex.org/I6498739"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Kishan Chand Gupta","raw_affiliation_strings":["Applied Statistics Unit, Indian Statistical Institute, Calcutta, India","Appl. Stat. Unit, Indian Stat. Inst., Kolkata"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Statistics Unit, Indian Statistical Institute, Calcutta, India","institution_ids":["https://openalex.org/I6498739"]},{"raw_affiliation_string":"Appl. Stat. Unit, Indian Stat. Inst., Kolkata","institution_ids":["https://openalex.org/I6498739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036784831","display_name":"Palash Sarkar","orcid":"https://orcid.org/0000-0002-5346-2650"},"institutions":[{"id":"https://openalex.org/I6498739","display_name":"Indian Statistical Institute","ror":"https://ror.org/00q2w1j53","country_code":"IN","type":"education","lineage":["https://openalex.org/I6498739"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Palash Sarkar","raw_affiliation_strings":["Applied Statistics Unit, Indian Statistical Institute, Calcutta, India","Appl. Stat. Unit, Indian Stat. Inst., Kolkata"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Statistics Unit, Indian Statistical Institute, Calcutta, India","institution_ids":["https://openalex.org/I6498739"]},{"raw_affiliation_string":"Appl. Stat. Unit, Indian Stat. Inst., Kolkata","institution_ids":["https://openalex.org/I6498739"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I6498739"],"apc_list":null,"apc_paid":null,"fwci":0.8883,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.81426172,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"55","issue":"3","first_page":"1354","last_page":"1359"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9991000294685364,"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":0.9991000294685364,"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/T10911","display_name":"Chemical Synthesis and Analysis","score":0.9811999797821045,"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"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9678999781608582,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/boolean-function","display_name":"Boolean function","score":0.7601561546325684},{"id":"https://openalex.org/keywords/walsh-function","display_name":"Walsh function","score":0.7599796056747437},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6272493600845337},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6108076572418213},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.5696324110031128},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.543472170829773},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.515512228012085},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.490695595741272},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.47473984956741333},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4263610243797302},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.37737104296684265},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23374205827713013},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20451173186302185},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1487576961517334}],"concepts":[{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.7601561546325684},{"id":"https://openalex.org/C164319782","wikidata":"https://www.wikidata.org/wiki/Q1934233","display_name":"Walsh function","level":2,"score":0.7599796056747437},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6272493600845337},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6108076572418213},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.5696324110031128},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.543472170829773},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.515512228012085},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.490695595741272},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.47473984956741333},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4263610243797302},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37737104296684265},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23374205827713013},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20451173186302185},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1487576961517334},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2008.2011439","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2008.2011439","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":[{"id":"https://openalex.org/F4320325957","display_name":"Novo Nordisk Fonden","ror":"https://ror.org/04txyc737"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1565388220","https://openalex.org/W1588183317","https://openalex.org/W1606480398","https://openalex.org/W1997855358","https://openalex.org/W2011798878","https://openalex.org/W2012559723","https://openalex.org/W2039544376","https://openalex.org/W2042194938","https://openalex.org/W2112747630","https://openalex.org/W2593170163"],"related_works":["https://openalex.org/W1999860306","https://openalex.org/W1986517398","https://openalex.org/W2109998394","https://openalex.org/W2058288504","https://openalex.org/W4252281389","https://openalex.org/W2107037376","https://openalex.org/W4321353861","https://openalex.org/W4294811728","https://openalex.org/W1974664230","https://openalex.org/W1488612364"],"abstract_inverted_index":{"We":[0,47],"study":[1],"the":[2,5,9,19,23,30,43,61,73,79,108,129,152],"relationship":[3],"between":[4],"Walsh":[6,31,62,110,130],"transform":[7,32,63,111,131],"and":[8,53,87],"algebraic":[10,44,153],"normal":[11,45,154],"form":[12],"(ANF)":[13],"of":[14,22,39,69,78,136,138,144],"a":[15,27,34,65,133,141,147],"Boolean":[16],"function.":[17],"In":[18],"first":[20],"part":[21,77],"paper,":[24],"we":[25],"obtain":[26,56],"formula":[28,86],"for":[29,60],"at":[33,64],"certain":[35,118],"point":[36,66],"in":[37,67,99,151],"terms":[38,68,150],"parameters":[40,70],"derived":[41,71],"from":[42,72],"form.":[46,155],"use":[48,107],"previous":[49],"results":[50,114],"by":[51],"Carlet":[52],"Guillot":[54],"to":[55,83,91,106,123,127],"an":[57,89],"explicit":[58],"expression":[59],"ANF.":[74],"The":[75],"second":[76],"paper":[80],"is":[81,103,121],"devoted":[82],"simplify":[84],"this":[85],"develop":[88],"algorithm":[90,95,126],"evaluate":[92,128],"it.":[93],"This":[94],"can":[96],"be":[97],"applied":[98],"situations":[100],"where":[101],"it":[102,120],"practically":[104],"impossible":[105],"fast":[109],"algorithm.":[112],"Experimental":[113],"show":[115],"that":[116],"under":[117],"conditions":[119],"possible":[122],"execute":[124],"our":[125],"(at":[132],"small":[134],"set":[135],"points)":[137],"functions":[139],"on":[140],"few":[142,148],"scores":[143],"variables":[145],"having":[146],"hundred":[149]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
