{"id":"https://openalex.org/W2886008983","doi":"https://doi.org/10.3934/amc.2018029","title":"Hamming correlation of higher order","display_name":"Hamming correlation of higher order","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2886008983","doi":"https://doi.org/10.3934/amc.2018029","mag":"2886008983"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2018029","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2018029","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=aad8b501-9aa0-4ff6-b559-2888bcd27bfc","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/article/exportPdf?id=aad8b501-9aa0-4ff6-b559-2888bcd27bfc","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051069206","display_name":"Ming Su","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ming Su","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5056642780","display_name":"Arne Winterhof","orcid":"https://orcid.org/0000-0002-3863-1110"},"institutions":[{"id":"https://openalex.org/I4210158379","display_name":"Johann Radon Institute for Computational and Applied Mathematics","ror":"https://ror.org/05a94k872","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Arne Winterhof","raw_affiliation_strings":["Johann Radon Institute for Computational and Applied Mathematics, Altenberger Stra\u00dfe 69, A-4040 Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johann Radon Institute for Computational and Applied Mathematics, Altenberger Stra\u00dfe 69, A-4040 Linz, Austria","institution_ids":["https://openalex.org/I4210158379"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5051069206"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08915651,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"3","first_page":"505","last_page":"513"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9987000226974487,"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":0.9987000226974487,"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":0.989799976348877,"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/T12946","display_name":"Fractal and DNA sequence analysis","score":0.9659000039100647,"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/mathematics","display_name":"Mathematics","score":0.8326581716537476},{"id":"https://openalex.org/keywords/pseudorandomness","display_name":"Pseudorandomness","score":0.8119348287582397},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.7665406465530396},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.7204792499542236},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.6377429366111755},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6220443844795227},{"id":"https://openalex.org/keywords/autocorrelation","display_name":"Autocorrelation","score":0.6110445261001587},{"id":"https://openalex.org/keywords/correlation","display_name":"Correlation","score":0.5111420750617981},{"id":"https://openalex.org/keywords/hamming-bound","display_name":"Hamming bound","score":0.5025091171264648},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4430510997772217},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3940221965312958},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.3892139196395874},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23323720693588257},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1592790186405182},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.0722404420375824},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05688181519508362},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05085289478302002}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8326581716537476},{"id":"https://openalex.org/C19086982","wikidata":"https://www.wikidata.org/wiki/Q2115856","display_name":"Pseudorandomness","level":3,"score":0.8119348287582397},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.7665406465530396},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.7204792499542236},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.6377429366111755},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6220443844795227},{"id":"https://openalex.org/C5297727","wikidata":"https://www.wikidata.org/wiki/Q786970","display_name":"Autocorrelation","level":2,"score":0.6110445261001587},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.5111420750617981},{"id":"https://openalex.org/C166530166","wikidata":"https://www.wikidata.org/wiki/Q1970635","display_name":"Hamming bound","level":5,"score":0.5025091171264648},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4430510997772217},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3940221965312958},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.3892139196395874},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23323720693588257},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1592790186405182},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.0722404420375824},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05688181519508362},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05085289478302002},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2018029","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2018029","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=aad8b501-9aa0-4ff6-b559-2888bcd27bfc","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/amc.2018029","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2018029","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=aad8b501-9aa0-4ff6-b559-2888bcd27bfc","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4300000071525574,"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W34086506","https://openalex.org/W145145483","https://openalex.org/W1515061872","https://openalex.org/W1567281213","https://openalex.org/W1972186222","https://openalex.org/W2003906679","https://openalex.org/W2023042503","https://openalex.org/W2027304562","https://openalex.org/W2030658611","https://openalex.org/W2031692310","https://openalex.org/W2050569702","https://openalex.org/W2055616008","https://openalex.org/W2063658803","https://openalex.org/W2076251051","https://openalex.org/W2104430950","https://openalex.org/W2119283406","https://openalex.org/W2120765143","https://openalex.org/W2129568979","https://openalex.org/W2132474171","https://openalex.org/W2132526163","https://openalex.org/W2171089917","https://openalex.org/W2245631212","https://openalex.org/W2419676999","https://openalex.org/W2485820268","https://openalex.org/W2492473084","https://openalex.org/W2548318495","https://openalex.org/W4239691897"],"related_works":["https://openalex.org/W2371167013","https://openalex.org/W1964096323","https://openalex.org/W4302771537","https://openalex.org/W2740543340","https://openalex.org/W2119135810","https://openalex.org/W2951416090","https://openalex.org/W2105471374","https://openalex.org/W2008960744","https://openalex.org/W2014631828","https://openalex.org/W2142293082"],"abstract_inverted_index":{"We":[0,22,83],"introduce":[1],"a":[2,58],"new":[3],"measure":[4,40,53,60],"of":[5,11,30,37,41,54,65,86,100,119],"pseudorandomness,":[6],"the":[7,16,24,27,34,38,51,62,69],"(periodic)":[8],"Hamming":[9,17,28,63,90,98],"correlation":[10,29,39,52,64,91,99],"order":[12,31,42,55,66,101],"$\\ell$":[13,32,43,56,102],"which":[14],"generalizes":[15],"autocorrelation":[18],"($\\ell":[19],"=":[20],"2$).":[21],"analyze":[23,84],"relation":[25],"between":[26],"and":[33,47,76,92],"periodic":[35],"analog":[36],"introduced":[44],"by":[45],"Mauduit":[46],"S\u00e1rk\u00f6zy.":[48],"Roughly":[49],"speaking,":[50],"is":[57],"finer":[59],"than":[61],"$\\ell$.":[67],"However,":[68],"latter":[70],"can":[71],"be":[72],"much":[73],"faster":[74],"calculated":[75],"still":[77],"detects":[78],"some":[79,104,111],"undesirable":[80,112],"linear":[81,113],"structures.":[82],"examples":[85],"sequences":[87],"with":[88],"optimal":[89],"show":[93],"that":[94],"they":[95,109],"have":[96,110],"large":[97],"for":[103],"very":[105],"small":[106],"$\\ell&gt;2$.":[107],"Thus":[108],"structures,":[114],"in":[115,117],"particular":[116],"view":[118],"cryptographic":[120],"applications":[121],"such":[122],"as":[123],"secure":[124],"communications.":[125]},"counts_by_year":[],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}
