{"id":"https://openalex.org/W2034204432","doi":"https://doi.org/10.1109/isit.2012.6283038","title":"Optimal family of q-ary codes obtained from a substructure of generalised Hadamard matrices","display_name":"Optimal family of q-ary codes obtained from a substructure of generalised Hadamard matrices","publication_year":2012,"publication_date":"2012-07-01","ids":{"openalex":"https://openalex.org/W2034204432","doi":"https://doi.org/10.1109/isit.2012.6283038","mag":"2034204432"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2012.6283038","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2012.6283038","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Symposium on Information Theory Proceedings","raw_type":"proceedings-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/A5005728627","display_name":"Carl Bracken","orcid":null},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Carl Bracken","raw_affiliation_strings":["Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371"],"affiliations":[{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088037430","display_name":"Yeow Meng Chee","orcid":"https://orcid.org/0000-0001-7823-8068"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Yeow Meng Chee","raw_affiliation_strings":["Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371"],"affiliations":[{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110941535","display_name":"Punarbasu Purkayastha","orcid":null},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Punarbasu Purkayastha","raw_affiliation_strings":["Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371"],"affiliations":[{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005728627"],"corresponding_institution_ids":["https://openalex.org/I172675005"],"apc_list":null,"apc_paid":null,"fwci":0.4421,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.72399745,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2","issue":null,"first_page":"116","last_page":"119"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9995999932289124,"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":0.9937999844551086,"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/algorithm","display_name":"Algorithm","score":0.3104267120361328},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26236963272094727}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3104267120361328},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26236963272094727}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/isit.2012.6283038","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2012.6283038","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Symposium on Information Theory Proceedings","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.719.1979","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.719.1979","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www1.spms.ntu.edu.sg/%7Eymchee/papers/hadamard.pdf","raw_type":"text"},{"id":"pmh:oai:dr.ntu.edu.sg:10356/102595","is_oa":false,"landing_page_url":"https://hdl.handle.net/10356/102595","pdf_url":null,"source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Conference Paper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1945608836","https://openalex.org/W1967009268","https://openalex.org/W2004485321","https://openalex.org/W2012023361","https://openalex.org/W2017740623","https://openalex.org/W2024389241","https://openalex.org/W2061269538","https://openalex.org/W2073419790"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2052122378","https://openalex.org/W2544423928","https://openalex.org/W2062023542","https://openalex.org/W4313731559"],"abstract_inverted_index":{"In":[0],"this":[1],"article":[2],"we":[3],"construct":[4],"an":[5],"infinite":[6],"family":[7,83,141],"of":[8,87,130,139,150],"linear":[9],"error":[10],"correcting":[11],"codes":[12,92,123],"over":[13],"F":[14],"<sub":[15,73,110],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[16,29,34,39,44,50,55,60,65,70,74,97,106,111,119],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">q</sub>":[17,75],"for":[18,77],"any":[19,78],"prime":[20],"power":[21],"q.":[22],"The":[23,122,137],"code":[24],"parameters":[25,94],"are":[26,124],"[q":[27],"<sup":[28,33,38,43,49,54,59,64,69,96,105,118],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2t</sup>":[30,51],"+":[31,52,57,102],"q":[32,37,42,48,53,58,68],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">t-1</sup>":[35,61,120],"-":[36,41,62,67,99,108],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2t-1</sup>":[40,66],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">t</sup>":[45,71],",":[46,76,113],"2t+1,":[47],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2t-2</sup>":[56],"2q":[63],"]":[72],"positive":[79],"integer":[80],"t.":[81],"This":[82],"is":[84,142],"a":[85,128,131,146],"generalisation":[86,149],"the":[88,140,151,159],"optimal":[89],"self-complementary":[90],"binary":[91],"with":[93],"[2u":[95],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[98,107],"u,":[100],"2t":[101],"1,":[103,157],"u":[104,115],"u]":[109],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[112],"where":[114],"=":[116,164],"2":[117],".":[121],"obtained":[125],"by":[126,144],"considering":[127],"submatrix":[129],"specially":[132],"constructed":[133],"generalised":[134],"Hadamard":[135],"matrix.":[136],"optimality":[138],"confirmed":[143],"using":[145],"recently":[147],"derived":[148],"Grey-Rankin":[152],"bound":[153,161],"when":[154,162],"t":[155,163],">;":[156],"and":[158],"Griesmer":[160],"1.":[165]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}