{"id":"https://openalex.org/W2152841761","doi":"https://doi.org/10.1142/s179383091250022x","title":"SOME CONSTRUCTIONS OF MUTUALLY ORTHOGONAL LATIN SQUARES AND SUPERIMPOSED CODES","display_name":"SOME CONSTRUCTIONS OF MUTUALLY ORTHOGONAL LATIN SQUARES AND SUPERIMPOSED CODES","publication_year":2012,"publication_date":"2012-08-06","ids":{"openalex":"https://openalex.org/W2152841761","doi":"https://doi.org/10.1142/s179383091250022x","mag":"2152841761"},"language":"en","primary_location":{"id":"doi:10.1142/s179383091250022x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s179383091250022x","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073611240","display_name":"Jennifer Seberry","orcid":"https://orcid.org/0000-0002-9558-4293"},"institutions":[{"id":"https://openalex.org/I204824540","display_name":"University of Wollongong","ror":"https://ror.org/00jtmb277","country_code":"AU","type":"education","lineage":["https://openalex.org/I204824540"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"JENNIFER SEBERRY","raw_affiliation_strings":["School of Computer Science and Software Engineering, University of Wollongong, Australia"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Software Engineering, University of Wollongong, Australia","institution_ids":["https://openalex.org/I204824540"]}]},{"author_position":"last","author":{"id":null,"display_name":"DONGVU TONIEN","orcid":null},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]},{"id":"https://openalex.org/I2802631561","display_name":"Australian Mathematical Sciences Institute","ror":"https://ror.org/00yn60108","country_code":"AU","type":"other","lineage":["https://openalex.org/I2802631561"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"DONGVU TONIEN","raw_affiliation_strings":["Mathematical Sciences Institute, Australian National University, Australia"],"affiliations":[{"raw_affiliation_string":"Mathematical Sciences Institute, Australian National University, Australia","institution_ids":["https://openalex.org/I2802631561","https://openalex.org/I118347636"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073611240"],"corresponding_institution_ids":["https://openalex.org/I204824540"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.13916367,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"04","issue":"03","first_page":"1250022","last_page":"1250022"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9997000098228455,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/orthogonal-array","display_name":"Orthogonal array","score":0.6897873878479004},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.6230082511901855},{"id":"https://openalex.org/keywords/combinatorial-design","display_name":"Combinatorial design","score":0.6163902282714844},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5962740778923035},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5758775472640991},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.46444278955459595},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4637176990509033},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45723021030426025},{"id":"https://openalex.org/keywords/coding-theory","display_name":"Coding theory","score":0.450168639421463},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.43534091114997864},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.43387794494628906},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.42170530557632446},{"id":"https://openalex.org/keywords/reed\u2013solomon-error-correction","display_name":"Reed\u2013Solomon error correction","score":0.4101578891277313},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.3505670428276062},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.337729811668396},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32539618015289307},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32529133558273315},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.13168904185295105},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11817315220832825},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.059047967195510864}],"concepts":[{"id":"https://openalex.org/C42632107","wikidata":"https://www.wikidata.org/wiki/Q2031860","display_name":"Orthogonal array","level":3,"score":0.6897873878479004},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.6230082511901855},{"id":"https://openalex.org/C122451846","wikidata":"https://www.wikidata.org/wiki/Q5150824","display_name":"Combinatorial design","level":2,"score":0.6163902282714844},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5962740778923035},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5758775472640991},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.46444278955459595},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4637176990509033},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45723021030426025},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.450168639421463},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.43534091114997864},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.43387794494628906},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.42170530557632446},{"id":"https://openalex.org/C78065487","wikidata":"https://www.wikidata.org/wiki/Q1061598","display_name":"Reed\u2013Solomon error correction","level":5,"score":0.4101578891277313},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.3505670428276062},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.337729811668396},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32539618015289307},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32529133558273315},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.13168904185295105},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11817315220832825},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.059047967195510864},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C83469408","wikidata":"https://www.wikidata.org/wiki/Q2036525","display_name":"Taguchi methods","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s179383091250022x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s179383091250022x","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"},{"id":"pmh:oai:ro.uow.edu.au:eispapers-1583","is_oa":false,"landing_page_url":"https://ro.uow.edu.au/eispapers/577","pdf_url":null,"source":{"id":"https://openalex.org/S4306400510","display_name":"Research Online (University of Wollongong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I204824540","host_organization_name":"University of Wollongong","host_organization_lineage":["https://openalex.org/I204824540"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty of Engineering and Information Sciences - Papers: Part A","raw_type":"article"},{"id":"pmh:oai:figshare.com:article/27762792","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/27762792","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W428388907","https://openalex.org/W1968160142","https://openalex.org/W1994662217","https://openalex.org/W2042090350","https://openalex.org/W2059022735","https://openalex.org/W2077263982","https://openalex.org/W2088379485","https://openalex.org/W2090388266","https://openalex.org/W2106329929","https://openalex.org/W2149588351","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3088883112","https://openalex.org/W2083498121","https://openalex.org/W4298280412","https://openalex.org/W2963870842","https://openalex.org/W2625239423","https://openalex.org/W2060062708","https://openalex.org/W1517974013","https://openalex.org/W4256043838","https://openalex.org/W3085073875","https://openalex.org/W4250675451"],"abstract_inverted_index":{"Superimposed":[0],"codes":[1,68,119,125],"is":[2,26],"a":[3,27,43,61,105,111,131],"special":[4],"combinatorial":[5,29,132],"structure":[6],"that":[7,31],"has":[8,32],"many":[9],"applications":[10],"in":[11,86],"information":[12],"theory,":[13],"data":[14],"communication":[15],"and":[16,58,126],"cryptography.":[17],"On":[18],"the":[19,82,87,91],"other":[20],"hand,":[21],"mutually":[22,54,75],"orthogonal":[23,55,76],"latin":[24,56,77],"squares":[25,57],"beautiful":[28],"object":[30],"deep":[33],"connection":[34,44],"with":[35],"design":[36],"theory.":[37],"In":[38],"this":[39,100],"paper,":[40],"we":[41,59,102],"draw":[42],"between":[45],"these":[46],"two":[47],"structures.":[48],"We":[49],"give":[50],"explicit":[51],"construction":[52,129],"of":[53,63,84,117],"show":[60],"method":[62],"generating":[64],"new":[65,92,128],"larger":[66],"superimposed":[67,108,118],"from":[69,110],"an":[70],"existing":[71,88],"one":[72],"by":[73],"using":[74,99],"squares.":[78],"If":[79],"n":[80,95],"denotes":[81],"number":[83],"codewords":[85],"code":[89,93,109],"then":[90],"contains":[94],"2":[96],"codewords.":[97],"Recursively,":[98],"method,":[101],"can":[103],"construct":[104],"very":[106],"large":[107],"small":[112],"simple":[113],"code.":[114],"Well-known":[115],"constructions":[116],"are":[120],"based":[121],"on":[122],"algebraic":[123],"Reed\u2013Solomon":[124],"our":[127],"gives":[130],"alternative":[133],"approach.":[134]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}