{"id":"https://openalex.org/W7161779441","doi":"https://doi.org/10.48550/arxiv.2605.19268","title":"Sequences with thirteen-valued cross correlations","display_name":"Sequences with thirteen-valued cross correlations","publication_year":2026,"publication_date":"2026-05-19","ids":{"openalex":"https://openalex.org/W7161779441","doi":"https://doi.org/10.48550/arxiv.2605.19268"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.19268","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.19268","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.19268","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135371529","display_name":"Yuehui Cui","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cui, Yuehui","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5136562509","display_name":"Jinquan Luo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luo, Jinquan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.8144999742507935,"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":0.8144999742507935,"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/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.029400000348687172,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11720","display_name":"Probability and Risk Models","score":0.026399999856948853,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/correlation","display_name":"Correlation","score":0.5403000116348267},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.5289000272750854},{"id":"https://openalex.org/keywords/cross-correlation","display_name":"Cross-correlation","score":0.48809999227523804},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4652000069618225},{"id":"https://openalex.org/keywords/correlation-coefficient","display_name":"Correlation coefficient","score":0.25690001249313354}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5773000121116638},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.5403000116348267},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5289000272750854},{"id":"https://openalex.org/C163018871","wikidata":"https://www.wikidata.org/wiki/Q1302587","display_name":"Cross-correlation","level":2,"score":0.48809999227523804},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4652000069618225},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.28279998898506165},{"id":"https://openalex.org/C2780092901","wikidata":"https://www.wikidata.org/wiki/Q3433612","display_name":"Correlation coefficient","level":2,"score":0.25690001249313354},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.24150000512599945},{"id":"https://openalex.org/C98385598","wikidata":"https://www.wikidata.org/wiki/Q1339385","display_name":"Empirical distribution function","level":2,"score":0.23559999465942383},{"id":"https://openalex.org/C106366893","wikidata":"https://www.wikidata.org/wiki/Q5454862","display_name":"Fisher transformation","level":3,"score":0.23250000178813934}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.19268","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.19268","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.19268","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.19268","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1,57],"paper,":[2],"we":[3],"completely":[4],"determine":[5],"the":[6,46,52,59,63],"cross":[7,47,64],"correlation":[8,48,65],"distribution":[9,66],"between":[10],"an":[11],"$m$-sequence":[12],"$(s_t)$":[13],"of":[14,54,67],"period":[15],"$p^n-1$":[16],"and":[17,36],"its":[18],"$d$-decimated":[19],"sequence":[20],"$(s_{dt})$,":[21],"where":[22],"$d":[23],"=":[24],"\\frac{p^n-1}{3}":[25],"+":[26],"p^i$,":[27],"$p":[28],"\\equiv":[29],"1":[30],"\\pmod{3}$,":[31,35],"$\\frac{1}{3}p^{-i}(p^n-1)":[32],"\\not\\equiv":[33],"2":[34],"$0":[37],"\\leq":[38],"i":[39],"<":[40],"n$.":[41],"It":[42],"is":[43,49,58],"shown":[44],"that":[45,62],"$13$-valued.":[50],"To":[51],"best":[53],"our":[55],"knowledge,":[56],"first":[60],"time":[61],"so":[68],"many":[69],"values":[70],"has":[71],"been":[72],"determined.":[73]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-21T00:00:00"}