{"id":"https://openalex.org/W4213420445","doi":"https://doi.org/10.3934/amc.2022008","title":"Balanced ($\\mathbb{Z} _{2u}\\times \\mathbb{Z}_{38v}$, {3, 4, 5}, 1) difference packings and related codes","display_name":"Balanced ($\\mathbb{Z} _{2u}\\times \\mathbb{Z}_{38v}$, {3, 4, 5}, 1) difference packings and related codes","publication_year":2022,"publication_date":"2022-02-24","ids":{"openalex":"https://openalex.org/W4213420445","doi":"https://doi.org/10.3934/amc.2022008"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2022008","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2022008","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=fd1b648b-ab60-4304-93dd-744070118af4","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":null,"license_id":null,"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=fd1b648b-ab60-4304-93dd-744070118af4","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081780466","display_name":"Hengming Zhao","orcid":"https://orcid.org/0000-0001-5123-4745"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hengming Zhao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035284864","display_name":"Rongcun Qin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rongcun Qin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5065849788","display_name":"Dianhua Wu","orcid":"https://orcid.org/0000-0002-2966-0606"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dianhua Wu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01050875,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"1","first_page":"163","last_page":"178"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":1.0,"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/T11130","display_name":"Coding theory and cryptography","score":0.992900013923645,"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/T11213","display_name":"Genomic variations and chromosomal abnormalities","score":0.9279999732971191,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"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":0.7267484664916992},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5699760913848877},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3419919013977051}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7267484664916992},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5699760913848877},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3419919013977051}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2022008","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2022008","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=fd1b648b-ab60-4304-93dd-744070118af4","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":null,"license_id":null,"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.2022008","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2022008","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=fd1b648b-ab60-4304-93dd-744070118af4","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":null,"license_id":null,"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":42,"referenced_works":["https://openalex.org/W1449397575","https://openalex.org/W1486301575","https://openalex.org/W1502206514","https://openalex.org/W1607001153","https://openalex.org/W1876033228","https://openalex.org/W1981204300","https://openalex.org/W1986813019","https://openalex.org/W1994975665","https://openalex.org/W2020546350","https://openalex.org/W2028683584","https://openalex.org/W2032751380","https://openalex.org/W2034206695","https://openalex.org/W2043682849","https://openalex.org/W2060864923","https://openalex.org/W2070341335","https://openalex.org/W2086298232","https://openalex.org/W2090856277","https://openalex.org/W2098412403","https://openalex.org/W2103842696","https://openalex.org/W2122816622","https://openalex.org/W2134600214","https://openalex.org/W2140865252","https://openalex.org/W2157090025","https://openalex.org/W2157749060","https://openalex.org/W2162383377","https://openalex.org/W2166010191","https://openalex.org/W2168287084","https://openalex.org/W2169410529","https://openalex.org/W2237738955","https://openalex.org/W2313315680","https://openalex.org/W2558966465","https://openalex.org/W2782085565","https://openalex.org/W2784011404","https://openalex.org/W2912323067","https://openalex.org/W2938586382","https://openalex.org/W2962834843","https://openalex.org/W2963616009","https://openalex.org/W2964262788","https://openalex.org/W3118270720","https://openalex.org/W3202530134","https://openalex.org/W4205545339","https://openalex.org/W4288400169"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"<p":[0],"style='text-indent:20px;'>Let":[1],"<inline-formula><tex-math":[2,6,14,29,38,67,77,85,98,103,117,128,140],"id=\"M1\">\\begin{document}$":[3],"m":[4],"$\\end{document}</tex-math></inline-formula>,":[5,134],"id=\"M2\">\\begin{document}$":[7],"n":[8],"$\\end{document}</tex-math></inline-formula>":[9,17,32,70,82],"be":[10,71,92],"positive":[11,21],"integers,":[12],"and":[13,46,135],"id=\"M3\">\\begin{document}$":[15],"K":[16],"a":[18,75,96],"set":[19],"of":[20,62,115],"integers":[22],"with":[23,59,127],"size":[24],"greater":[25],"than":[26],"2.":[27],"An":[28],"id=\"M4\">\\begin{document}$":[30],"(m,n,K,1)":[31,40,100],"optical":[33,54],"orthogonal":[34],"signature":[35],"pattern":[36],"code,":[37],"id=\"M5\">\\begin{document}$":[39],"$\\end{document}</tex-math></inline-formula>-OOSPC,":[41],"was":[42],"introduced":[43],"by":[44],"Kwong":[45],"Yang":[47],"for":[48],"2-D":[49],"image":[50],"transmission":[51],"in":[52],"multicore-fiber":[53],"code-division":[55],"multiple-access":[56],"(OCDMA)":[57],"networks":[58],"multiple":[60],"quality":[61],"services":[63],"(QoS)":[64],"requirement.":[65],"Let":[66],"id=\"M6\">\\begin{document}$":[68],"G":[69,105],"an":[72],"additive":[73],"group,":[74],"balanced":[76,97,139],"id=\"M7\">\\begin{document}$":[78],"(G,":[79,87],"K,":[80,88],"1)":[81,89],"difference":[83],"packing,":[84],"id=\"M8\">\\begin{document}$":[86],"$\\end{document}</tex-math></inline-formula>-BDP,":[90],"can":[91],"used":[93],"to":[94],"construct":[95],"id=\"M9\">\\begin{document}$":[99],"$\\end{document}</tex-math></inline-formula>-OOSPC":[101],"when":[102],"id=\"M10\">\\begin{document}$":[104],"=":[106],"{\\mathbb{Z}}_m\\times":[107],"{\\mathbb{Z}}_n":[108],"$\\end{document}</tex-math></inline-formula>.":[109],"In":[110],"this":[111],"paper,":[112],"the":[113,136],"existences":[114],"optimal":[116,138],"id=\"M11\">\\begin{document}$":[118],"(":[119],"{\\mathbb{Z}}_{2u}\\times":[120],"{\\mathbb{Z}}_{38v},":[121],"\\{3,4,5\\},1)":[122],"$\\end{document}</tex-math></inline-formula>-BDPs":[123],"are":[124,145],"completely":[125],"solved":[126],"id=\"M12\">\\begin{document}$":[129],"u,":[130],"\\":[131],"v\\equiv":[132],"1\\pmod2":[133],"corresponding":[137],"id=\"M13\">\\begin{document}$":[141],"(2u,":[142],"38v,\\{3,4,5\\},1)":[143],"$\\end{document}</tex-math></inline-formula>-OOSPCs":[144],"also":[146],"obtained.":[147]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}