{"id":"https://openalex.org/W2035311227","doi":"https://doi.org/10.1137/080717079","title":"Fourier Spectra of Binomial APN Functions","display_name":"Fourier Spectra of Binomial APN Functions","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2035311227","doi":"https://doi.org/10.1137/080717079","mag":"2035311227"},"language":"ca","primary_location":{"id":"doi:10.1137/080717079","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080717079","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","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/A5005728627","display_name":"Carl Bracken","orcid":null},"institutions":[{"id":"https://openalex.org/I1325784139","display_name":"Yahoo (United Kingdom)","ror":"https://ror.org/038p3gq39","country_code":"GB","type":"company","lineage":["https://openalex.org/I1325784139","https://openalex.org/I4210134091"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Carl Bracken","raw_affiliation_strings":["carlbracken@yahoo.com and ebyrne@ucd.ie and nadyaomarkin@gmail.com and gary.mcguire@ucd.ie#TAB#"],"affiliations":[{"raw_affiliation_string":"carlbracken@yahoo.com and ebyrne@ucd.ie and nadyaomarkin@gmail.com and gary.mcguire@ucd.ie#TAB#","institution_ids":["https://openalex.org/I1325784139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025217200","display_name":"Eimear Byrne","orcid":"https://orcid.org/0000-0002-1857-0365"},"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":"Eimear Byrne","raw_affiliation_strings":["university college dublin"],"affiliations":[{"raw_affiliation_string":"university college dublin","institution_ids":["https://openalex.org/I100930933"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018122428","display_name":"Nadya Markin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nadya Markin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5049086257","display_name":"Gary McGuire","orcid":"https://orcid.org/0000-0003-2105-9792"},"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":"Gary McGuire","raw_affiliation_strings":["university college dublin"],"affiliations":[{"raw_affiliation_string":"university college dublin","institution_ids":["https://openalex.org/I100930933"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5005728627"],"corresponding_institution_ids":["https://openalex.org/I1325784139"],"apc_list":null,"apc_paid":null,"fwci":0.4516,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.72821963,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"23","issue":"2","first_page":"596","last_page":"608"},"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9986000061035156,"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":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bch-code","display_name":"BCH code","score":0.8380230665206909},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8262981176376343},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.6835655570030212},{"id":"https://openalex.org/keywords/binomial","display_name":"Binomial (polynomial)","score":0.6833034753799438},{"id":"https://openalex.org/keywords/gaussian-binomial-coefficient","display_name":"Gaussian binomial coefficient","score":0.5278206467628479},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.4847838282585144},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4467872381210327},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4397304356098175},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.43485406041145325},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.430764377117157},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37452125549316406},{"id":"https://openalex.org/keywords/negative-binomial-distribution","display_name":"Negative binomial distribution","score":0.3373830318450928},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2659849226474762},{"id":"https://openalex.org/keywords/error-detection-and-correction","display_name":"Error detection and correction","score":0.21286830306053162},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2058313488960266},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18595284223556519},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17993056774139404}],"concepts":[{"id":"https://openalex.org/C42276685","wikidata":"https://www.wikidata.org/wiki/Q795705","display_name":"BCH code","level":3,"score":0.8380230665206909},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8262981176376343},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6835655570030212},{"id":"https://openalex.org/C2781315470","wikidata":"https://www.wikidata.org/wiki/Q193623","display_name":"Binomial (polynomial)","level":2,"score":0.6833034753799438},{"id":"https://openalex.org/C139505817","wikidata":"https://www.wikidata.org/wiki/Q5527834","display_name":"Gaussian binomial coefficient","level":4,"score":0.5278206467628479},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4847838282585144},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4467872381210327},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4397304356098175},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.43485406041145325},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.430764377117157},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37452125549316406},{"id":"https://openalex.org/C199335787","wikidata":"https://www.wikidata.org/wiki/Q743364","display_name":"Negative binomial distribution","level":3,"score":0.3373830318450928},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2659849226474762},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.21286830306053162},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2058313488960266},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18595284223556519},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17993056774139404},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/080717079","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080717079","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:eprints.maynoothuniversity.ie:2703","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401432","display_name":"Maynooth University ePrints and eTheses Archive (Maynooth University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I157286207","host_organization_name":"National University of Ireland, Maynooth","host_organization_lineage":["https://openalex.org/I157286207"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.314.2427","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.314.2427","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/0803.3781v1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1485694296","https://openalex.org/W1528065150","https://openalex.org/W1587687098","https://openalex.org/W1977206724","https://openalex.org/W2024729203","https://openalex.org/W2089606264","https://openalex.org/W2097345111","https://openalex.org/W2100083939","https://openalex.org/W2156979688","https://openalex.org/W2163447078","https://openalex.org/W2173356534","https://openalex.org/W2397088619","https://openalex.org/W2949270442"],"related_works":["https://openalex.org/W2305431308","https://openalex.org/W3207115261","https://openalex.org/W2021262032","https://openalex.org/W2951403411","https://openalex.org/W2058976745","https://openalex.org/W4366831151","https://openalex.org/W4225635267","https://openalex.org/W4289107413","https://openalex.org/W3214798365","https://openalex.org/W2010957781"],"abstract_inverted_index":{"In":[0],"this":[1,21],"paper":[2],"we":[3],"compute":[4],"the":[5,23,26,29,50,55,76,80],"Fourier":[6],"spectra":[7],"of":[8,20,25,28,64,66,75,79],"some":[9],"recently":[10],"discovered":[11],"binomial":[12],"almost":[13],"perfect":[14],"nonlinear":[15],"(APN)":[16],"functions.":[17,81],"One":[18],"consequence":[19,39],"is":[22,40],"determination":[24],"nonlinearity":[27],"functions,":[30],"which":[31],"measures":[32],"their":[33],"resistance":[34],"to":[35,46],"linear":[36],"cryptanalysis.":[37],"Another":[38],"that":[41],"certain":[42],"error-correcting":[43],"codes":[44],"related":[45],"these":[47],"functions":[48],"have":[49],"same":[51],"weight":[52],"distribution":[53],"as":[54],"2-error-correcting":[56],"Bose\u2013Chaudury\u2013Hocquenghem":[57],"(BCH)":[58],"code.":[59],"Furthermore,":[60],"for":[61],"field":[62],"extensions":[63],"$\\mathbb{F}_2$":[65],"odd":[67],"degree,":[68],"our":[69],"results":[70],"provide":[71],"an":[72],"alternative":[73],"proof":[74],"APN":[77],"property":[78]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}