{"id":"https://openalex.org/W2588577247","doi":"https://doi.org/10.3934/amc.2017012","title":"More constructions of near optimal codebooks associated with binary sequences","display_name":"More constructions of near optimal codebooks associated with binary sequences","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2588577247","doi":"https://doi.org/10.3934/amc.2017012","mag":"2588577247"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2017012","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2017012","pdf_url":null,"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://doi.org/10.3934/amc.2017012","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026635882","display_name":"Xiwang Cao","orcid":"https://orcid.org/0000-0002-6950-8588"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Xiwang Cao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029618079","display_name":"Wun-Seng Chou","orcid":null},"institutions":[{"id":"https://openalex.org/I87354575","display_name":"National Chengchi University","ror":"https://ror.org/03rqk8h36","country_code":"TW","type":"education","lineage":["https://openalex.org/I87354575"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Wun-Seng Chou","raw_affiliation_strings":["Institute of Mathematics, Academia Sinica, and Department of Math, National Chengchi University, Taipei 115, Taiwan"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Academia Sinica, and Department of Math, National Chengchi University, Taipei 115, Taiwan","institution_ids":["https://openalex.org/I87354575"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074201509","display_name":"Xiyong Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210119388","display_name":"Zhejiang Science and Technology Information Institute","ror":"https://ror.org/02rzte064","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210119388"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiyong Zhang","raw_affiliation_strings":["Department of Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou, Henan 450002, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou, Henan 450002, China","institution_ids":["https://openalex.org/I4210119388"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5026635882"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.0188,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.90557171,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"11","issue":"1","first_page":"187","last_page":"202"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9998000264167786,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9975000023841858,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.9945999979972839,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/codebook","display_name":"Codebook","score":0.8669906854629517},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8398875594139099},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6986784934997559},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.6601805090904236},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.6308592557907104},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5835385322570801},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.5403026342391968},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5032302737236023},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.46110114455223083},{"id":"https://openalex.org/keywords/hadamard-matrix","display_name":"Hadamard matrix","score":0.4143970310688019},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40900731086730957},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24598708748817444},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.16289237141609192},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.1307952105998993},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09370675683021545}],"concepts":[{"id":"https://openalex.org/C127759330","wikidata":"https://www.wikidata.org/wiki/Q637416","display_name":"Codebook","level":2,"score":0.8669906854629517},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8398875594139099},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6986784934997559},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.6601805090904236},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6308592557907104},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5835385322570801},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.5403026342391968},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5032302737236023},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.46110114455223083},{"id":"https://openalex.org/C30463267","wikidata":"https://www.wikidata.org/wiki/Q1422682","display_name":"Hadamard matrix","level":3,"score":0.4143970310688019},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40900731086730957},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24598708748817444},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.16289237141609192},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.1307952105998993},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09370675683021545},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2017012","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2017012","pdf_url":null,"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.2017012","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2017012","pdf_url":null,"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W403434742","https://openalex.org/W1542496577","https://openalex.org/W1971917606","https://openalex.org/W1971946972","https://openalex.org/W1973378877","https://openalex.org/W1990773884","https://openalex.org/W1994984340","https://openalex.org/W2020089954","https://openalex.org/W2024483577","https://openalex.org/W2029835055","https://openalex.org/W2034168611","https://openalex.org/W2035289644","https://openalex.org/W2035469609","https://openalex.org/W2046938896","https://openalex.org/W2052633237","https://openalex.org/W2054194065","https://openalex.org/W2072704718","https://openalex.org/W2085618526","https://openalex.org/W2086869478","https://openalex.org/W2090432705","https://openalex.org/W2110673833","https://openalex.org/W2112446992","https://openalex.org/W2121743251","https://openalex.org/W2126085612","https://openalex.org/W2138238405","https://openalex.org/W2138548210","https://openalex.org/W2169607109","https://openalex.org/W2584020404","https://openalex.org/W2964184480","https://openalex.org/W3151140615","https://openalex.org/W6628614173"],"related_works":["https://openalex.org/W2038981428","https://openalex.org/W1976224891","https://openalex.org/W2768335563","https://openalex.org/W3154819821","https://openalex.org/W2740724818","https://openalex.org/W1971692815","https://openalex.org/W2054788067","https://openalex.org/W3118766198","https://openalex.org/W2010617738","https://openalex.org/W1995950135"],"abstract_inverted_index":{"An":[0],"$(N,":[1],"K)$":[2],"codebook":[3,28],"$\\mathcal{C}$":[4,145],"is":[5,53,60],"a":[6,13,27,31,54,77,84,88,157],"collection":[7],"of":[8,19,35,44,98,127,135,159],"unit":[9],"norm":[10],"vectors":[11,15,25],"in":[12,26],"$K$-dimensional":[14],"space.":[16],"In":[17],"applications":[18],"codebooks":[20,64,81,99,118,144],"such":[21],"as":[22,156],"CDMA,":[23],"those":[24],"should":[29],"have":[30],"small":[32],"maximum":[33,105],"magnitude":[34],"inner":[36,106],"products,":[37],"denoted":[38],"by":[39,119],"$I_{\\max}(\\mathcal{C})$,":[40,58],"between":[41],"any":[42],"pair":[43],"distinct":[45],"code":[46],"vectors.":[47],"Since":[48],"the":[49,66,104,136],"famous":[50],"Welch":[51,67],"bound":[52,56,68],"lower":[55],"on":[57,103,149],"it":[59],"desired":[61],"to":[62],"construct":[63,114],"meeting":[65],"strictly":[69],"or":[70],"asymptotically.":[71],"Recently,":[72],"N.":[73],"Y.":[74],"Yu":[75],"presents":[76],"method":[78],"for":[79],"constructing":[80],"associated":[82],"with":[83,100,146],"binary":[85,128],"sequence":[86],"from":[87,108],"$\\Phi$-transform":[89,137],"matrix.":[90],"Using":[91],"this":[92],"method,":[93],"he":[94],"discovers":[95],"new":[96],"classes":[97],"nontrivial":[101,147],"bounds":[102,148],"products":[107],"Fourier":[109],"and":[110],"Hadamard":[111],"matrices.":[112,138],"We":[113,122,130],"more":[115,125,133,143],"near":[116],"optimal":[117],"Yu's":[120,160],"idea.":[121],"first":[123],"provide":[124],"choices":[126,134],"sequences.":[129],"also":[131],"show":[132],"Therefore,":[139],"we":[140],"can":[141,154],"present":[142],"their":[150],"$I_{\\max}(\\mathcal{C})$.":[151],"Our":[152],"work":[153],"serve":[155],"complement":[158],"work.":[161]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}
