{"id":"https://openalex.org/W4281493197","doi":"https://doi.org/10.1142/s0129054122500101","title":"A Novel Approach Towards Degree and Walsh-Transform of Boolean Functions","display_name":"A Novel Approach Towards Degree and Walsh-Transform of Boolean Functions","publication_year":2022,"publication_date":"2022-05-24","ids":{"openalex":"https://openalex.org/W4281493197","doi":"https://doi.org/10.1142/s0129054122500101"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054122500101","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054122500101","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","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/A5100751057","display_name":"Sunil Kumar","orcid":"https://orcid.org/0000-0002-1953-6273"},"institutions":[{"id":"https://openalex.org/I1340206300","display_name":"Defence Research and Development Organisation","ror":"https://ror.org/05k37v296","country_code":"IN","type":"government","lineage":["https://openalex.org/I1340206300","https://openalex.org/I4210150591"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Sunil Kumar","raw_affiliation_strings":["Defence Research and Development Organisation, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Defence Research and Development Organisation, India","institution_ids":["https://openalex.org/I1340206300"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101398493","display_name":"Harshdeep Singh","orcid":"https://orcid.org/0000-0001-8500-9175"},"institutions":[{"id":"https://openalex.org/I1340206300","display_name":"Defence Research and Development Organisation","ror":"https://ror.org/05k37v296","country_code":"IN","type":"government","lineage":["https://openalex.org/I1340206300","https://openalex.org/I4210150591"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Harshdeep Singh","raw_affiliation_strings":["Defence Research and Development Organisation, India"],"raw_orcid":"https://orcid.org/0000-0001-8500-9175","affiliations":[{"raw_affiliation_string":"Defence Research and Development Organisation, India","institution_ids":["https://openalex.org/I1340206300"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003314698","display_name":"Gaurav Mittal","orcid":"https://orcid.org/0000-0002-5761-4287"},"institutions":[{"id":"https://openalex.org/I1340206300","display_name":"Defence Research and Development Organisation","ror":"https://ror.org/05k37v296","country_code":"IN","type":"government","lineage":["https://openalex.org/I1340206300","https://openalex.org/I4210150591"]},{"id":"https://openalex.org/I154851008","display_name":"Indian Institute of Technology Roorkee","ror":"https://ror.org/00582g326","country_code":"IN","type":"education","lineage":["https://openalex.org/I154851008"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Gaurav Mittal","raw_affiliation_strings":["Defence Research and Development Organisation, India","Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Defence Research and Development Organisation, India","institution_ids":["https://openalex.org/I1340206300"]},{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India","institution_ids":["https://openalex.org/I154851008"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101398493"],"corresponding_institution_ids":["https://openalex.org/I1340206300"],"apc_list":null,"apc_paid":null,"fwci":0.1387,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.52754138,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"33","issue":"05","first_page":"453","last_page":"479"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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":0.9997000098228455,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9959999918937683,"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/hadamard-transform","display_name":"Hadamard transform","score":0.84140944480896},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.8105902671813965},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6698713898658752},{"id":"https://openalex.org/keywords/walsh-function","display_name":"Walsh function","score":0.6634447574615479},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.551038920879364},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5089833736419678},{"id":"https://openalex.org/keywords/parity-function","display_name":"Parity function","score":0.5062186121940613},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.453166127204895},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4348200857639313},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.41857367753982544},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30222633481025696},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06998983025550842}],"concepts":[{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.84140944480896},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.8105902671813965},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6698713898658752},{"id":"https://openalex.org/C164319782","wikidata":"https://www.wikidata.org/wiki/Q1934233","display_name":"Walsh function","level":2,"score":0.6634447574615479},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.551038920879364},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5089833736419678},{"id":"https://openalex.org/C188183281","wikidata":"https://www.wikidata.org/wiki/Q2898309","display_name":"Parity function","level":4,"score":0.5062186121940613},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.453166127204895},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4348200857639313},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.41857367753982544},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30222633481025696},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06998983025550842}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129054122500101","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054122500101","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","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":17,"referenced_works":["https://openalex.org/W1480210121","https://openalex.org/W1576481659","https://openalex.org/W1588183317","https://openalex.org/W1880399293","https://openalex.org/W1995875735","https://openalex.org/W2004229705","https://openalex.org/W2024900297","https://openalex.org/W2121417875","https://openalex.org/W2137917781","https://openalex.org/W2313248807","https://openalex.org/W2506088122","https://openalex.org/W2806999765","https://openalex.org/W3150898570","https://openalex.org/W3188272707","https://openalex.org/W4205482204","https://openalex.org/W4241417662","https://openalex.org/W4318425176"],"related_works":["https://openalex.org/W2106622045","https://openalex.org/W2037737738","https://openalex.org/W1974664230","https://openalex.org/W2379318067","https://openalex.org/W1991921929","https://openalex.org/W4252281389","https://openalex.org/W4312990447","https://openalex.org/W353786736","https://openalex.org/W2157812200","https://openalex.org/W4294811728"],"abstract_inverted_index":{"Boolean":[0,24,59,75],"functions":[1,25],"are":[2],"fundamental":[3],"bricks":[4],"in":[5,11,41,81,88],"the":[6,20,30,47,54,79,99,102],"development":[7],"of":[8,22,58,83,101],"various":[9],"applications":[10],"Cryptography":[12],"and":[13,49,61,69,85],"Coding":[14],"theory":[15],"by":[16],"making":[17],"benefit":[18],"from":[19],"weights":[21,57],"related":[23,97],"(Walsh":[26],"spectrum).":[27],"Towards":[28],"this,":[29],"discrete":[31],"Fourier":[32,86],"transform":[33,87],"(Walsh\u2013Hadamard)":[34],"plays":[35],"a":[36],"pivotal":[37],"tool.":[38],"The":[39],"work":[40],"this":[42],"paper":[43],"is":[44],"dedicated":[45],"towards":[46],"algebraic":[48,103],"numerical":[50],"degrees,":[51],"together":[52],"with":[53],"relationship":[55],"between":[56],"function":[60],"their":[62],"Walsh":[63,67],"transforms.":[64],"We":[65,91],"introduce":[66],"matrices":[68],"generalize":[70],"them":[71],"to":[72,98],"any":[73],"arbitrary":[74],"function.":[76],"This":[77],"improves":[78],"complexity":[80],"computation":[82],"Walsh\u2013Hadamard":[84,107],"certain":[89],"cases.":[90],"also":[92],"discuss":[93],"some":[94],"useful":[95],"results":[96],"degree":[100],"normal":[104],"form":[105],"using":[106],"transform.":[108]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
