{"id":"https://openalex.org/W2068663342","doi":"https://doi.org/10.1109/tit.1984.1056864","title":"On certain projective geometry codes (Corresp.)","display_name":"On certain projective geometry codes (Corresp.)","publication_year":1984,"publication_date":"1984-03-01","ids":{"openalex":"https://openalex.org/W2068663342","doi":"https://doi.org/10.1109/tit.1984.1056864","mag":"2068663342"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1984.1056864","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1984.1056864","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-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/A5009502199","display_name":"Jimmy Huang","orcid":"https://orcid.org/0000-0003-1389-2223"},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"education","lineage":["https://openalex.org/I153718931"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"J. Huang","raw_affiliation_strings":["Department of Electrical Engineering, University of Ottawa, Ottawa, ONT, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Ottawa, Ottawa, ONT, Canada","institution_ids":["https://openalex.org/I153718931"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109677646","display_name":"S. Shiva","orcid":null},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"education","lineage":["https://openalex.org/I153718931"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"S. Shiva","raw_affiliation_strings":["Department of Electrical Engineering, University of Ottawa, Ottawa, ONT, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Ottawa, Ottawa, ONT, Canada","institution_ids":["https://openalex.org/I153718931"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046089126","display_name":"G. Seguin","orcid":null},"institutions":[{"id":"https://openalex.org/I51768193","display_name":"Royal Military College of Canada","ror":"https://ror.org/04yr71909","country_code":"CA","type":"education","lineage":["https://openalex.org/I51768193"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"G. Seguin","raw_affiliation_strings":["Department of Electrical Engineering, Royal Military College of Canada, Kingston, ONT, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Royal Military College of Canada, Kingston, ONT, Canada","institution_ids":["https://openalex.org/I51768193"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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":0.15467883,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"30","issue":"2","first_page":"385","last_page":"388"},"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/T10849","display_name":"Finite Group Theory Research","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.9879999756813049,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.4395018219947815},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.336877703666687},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32683897018432617},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.31493547558784485},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24908781051635742}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4395018219947815},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.336877703666687},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32683897018432617},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.31493547558784485},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24908781051635742}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1984.1056864","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1984.1056864","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1534925464","https://openalex.org/W1606480398","https://openalex.org/W2182112064","https://openalex.org/W2910918398"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W4391913857"],"abstract_inverted_index":{"LetVbe":[0],"an(n,":[1],"k,":[2],"d)binary":[3],"projective":[4],"geometry":[5],"code":[6,23],"withn":[7],"=":[8,13,32,56,157,160],"(q^{m}-1)/(q":[9],"-":[10,18,58,68,70,72],"1),":[11,73],"q":[12],"2^{s},":[14],"andd":[15],"\\geq":[16],"[(q^{m-r}-1)/(q":[17],"1)]":[19],"+":[20],"1.":[21],"This":[22],"isr-step":[24],"majority-logic":[25],"decodable.":[26],"With":[27],"reference":[28],"to":[29,130],"the":[30,43,54,75,78,81,84,98,103,112,150,154],"GF(q^{m})":[31],"\\{0,":[33],"1,":[34],"\\alpha":[35],",":[36,38,40],"\\alpha^{2}":[37],"\\cdots":[39],"\\alpha^{n(q-1)-1}":[41],"\\},":[42],"generator":[44],"polynomialg(X),":[45],"ofV,":[46],"has\\alpha^{\\nu}as":[47],"a":[48,91,121,131],"root":[49,92],"if":[50,117],"and":[51,141],"only":[52],"if\\nuhas":[53],"form\\nu":[55],"i(q":[57],"1)and\\max_{0":[59],"\\leq":[60,66],"l":[61],"<":[62],"s}":[63],"W_{q}(2^{l}":[64],"\\nu)":[65],"(m":[67],"r":[69],"1)(q":[71],"whereW_{q}(x)indicates":[74],"weight":[76],"of":[77,80,86,105,114,133],"radix-qrepresentation":[79],"numberx.":[82],"LetSbe":[83],"set":[85],"nonzero":[87],"numbers\\nu,":[88],"such":[89,101],"that\\alpha^{\\nu}is":[90],"ofg(X).":[93],"LetC_{1},":[94],"C_{2},":[95],"\\cdots,":[96],"C_{\\nu}be":[97],"cyclotomic":[99],"cosets":[100],"thatSis":[102],"union":[104],"these":[106],"cosets.":[107],"It":[108],"is":[109],"clear":[110],"that":[111,149],"process":[113],"findingg(X)becomes":[115],"simpler":[116],"we":[118,126],"can":[119,127],"find":[120],"representative":[122],"from":[123],"eachC_{i},":[124],"since":[125],"then":[128],"refer":[129],"table,":[132],"irreducible":[134],"factors,":[135],"as":[136],"given":[137],"by,":[138],"say,":[139],"Peterson":[140],"Weldon.":[142],"In":[143],"this":[144],"correspondence":[145],"it":[146],"was":[147],"determined":[148],"coset":[151],"representatives":[152],"for":[153],"cases":[155],"ofm-r":[156],"2,":[158,161],"withs":[159],"3,":[162],"andm-r=3,":[163],"withs=2.":[164]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}