{"id":"https://openalex.org/W4285180637","doi":"https://doi.org/10.1109/tit.2022.3180666","title":"New Infinite Family of Sequences Almost Over <i>Q</i> <sub>8</sub> With Ideal Autocorrelation","display_name":"New Infinite Family of Sequences Almost Over <i>Q</i> <sub>8</sub> With Ideal Autocorrelation","publication_year":2022,"publication_date":"2022-06-06","ids":{"openalex":"https://openalex.org/W4285180637","doi":"https://doi.org/10.1109/tit.2022.3180666"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2022.3180666","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3180666","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/A5101748228","display_name":"Yan Liu","orcid":"https://orcid.org/0000-0001-5604-1627"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yan Liu","raw_affiliation_strings":["School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003303649","display_name":"Xiaojun Zhang","orcid":"https://orcid.org/0000-0002-5928-9457"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaojun Zhang","raw_affiliation_strings":["School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063764941","display_name":"Shuhui Shen","orcid":"https://orcid.org/0000-0002-2958-9192"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuhui Shen","raw_affiliation_strings":["School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China","institution_ids":["https://openalex.org/I150229711"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101748228"],"corresponding_institution_ids":["https://openalex.org/I150229711"],"apc_list":null,"apc_paid":null,"fwci":0.1326,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.514573,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"68","issue":"10","first_page":"6881","last_page":"6887"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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":0.9998000264167786,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9894000291824341,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.6161926984786987},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.5567625164985657},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5152771472930908},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.49064889550209045},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.41145819425582886},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36466488242149353},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3454810678958893},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1857999861240387},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.13432326912879944}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6161926984786987},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.5567625164985657},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5152771472930908},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.49064889550209045},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41145819425582886},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36466488242149353},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3454810678958893},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1857999861240387},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.13432326912879944},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2022.3180666","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3180666","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":[{"id":"https://openalex.org/G2509265183","display_name":null,"funder_award_id":"61771004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1420467599","https://openalex.org/W1546467724","https://openalex.org/W1965510685","https://openalex.org/W1977299570","https://openalex.org/W1990773884","https://openalex.org/W2045043420","https://openalex.org/W2047980659","https://openalex.org/W2056891342","https://openalex.org/W2106689435","https://openalex.org/W2108550051","https://openalex.org/W2113980068","https://openalex.org/W2130080747","https://openalex.org/W2142957872","https://openalex.org/W2145693890","https://openalex.org/W2166137511","https://openalex.org/W2313497592","https://openalex.org/W2910516124","https://openalex.org/W2943388400"],"related_works":["https://openalex.org/W2029981401","https://openalex.org/W2740334431","https://openalex.org/W4212808623","https://openalex.org/W4301344670","https://openalex.org/W3093722106","https://openalex.org/W2013467167","https://openalex.org/W2963699585","https://openalex.org/W3123287700","https://openalex.org/W4293879768","https://openalex.org/W2123831997"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,15],"provide":[4],"the":[5,12,59],"left":[6],"and":[7,58,79],"right":[8],"Parseval":[9],"relations":[10],"over":[11,24],"quaternions.":[13],"Moreover,":[14],"construct":[16],"a":[17,41],"new":[18],"infinite":[19],"family":[20],"of":[21,43],"sequences":[22,60,65],"almost":[23],"<inline-formula":[25,34,47,69,82],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[26,35,48,70,83],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[27,36,49,71,84],"<tex-math":[28,37,50,72,85],"notation=\"LaTeX\">$Q_{8}":[29],"$":[30,90],"</tex-math></inline-formula>":[31,39,55,77,91],"with":[32],"period":[33],"notation=\"LaTeX\">$p$":[38],"by":[40],"generalization":[42],"Legendre":[44],"mapping,":[45],"where":[46],"notation=\"LaTeX\">$p\\equiv":[51,73,86],"1":[52,74],"\\pmod":[53,75,88],"{8}$":[54],"is":[56],"prime":[57],"have":[61],"ideal":[62],"autocorrelation.":[63],"The":[64],"are":[66],"symmetric":[67],"when":[68,81],"{16}$":[76],",":[78],"antisymmetric":[80],"9":[87],"{16}":[89],".":[92]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}