{"id":"https://openalex.org/W2027246034","doi":"https://doi.org/10.1109/tit.1983.1056616","title":"A note on maximum distance separable (optimal) codes (Corresp.)","display_name":"A note on maximum distance separable (optimal) codes (Corresp.)","publication_year":1983,"publication_date":"1983-01-01","ids":{"openalex":"https://openalex.org/W2027246034","doi":"https://doi.org/10.1109/tit.1983.1056616","mag":"2027246034"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1983.1056616","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1983.1056616","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/A5024229936","display_name":"L. R. Vermani","orcid":null},"institutions":[{"id":"https://openalex.org/I178000100","display_name":"Kurukshetra University","ror":"https://ror.org/019bzvf55","country_code":"IN","type":"education","lineage":["https://openalex.org/I178000100"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"L. Vermani","raw_affiliation_strings":["Department of Mathematics, Kurukshetra University, Kurukshetra, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Kurukshetra University, Kurukshetra, India","institution_ids":["https://openalex.org/I178000100"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055337631","display_name":"Shilpa Jindal","orcid":null},"institutions":[{"id":"https://openalex.org/I3129549910","display_name":"University B.T. & Evening College","ror":"https://ror.org/02c5dz126","country_code":"IN","type":"education","lineage":["https://openalex.org/I3129549910"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"S. Jindal","raw_affiliation_strings":["M. D. University Evening College, Rohtak, India"],"affiliations":[{"raw_affiliation_string":"M. D. University Evening College, Rohtak, India","institution_ids":["https://openalex.org/I3129549910"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024229936"],"corresponding_institution_ids":["https://openalex.org/I178000100"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.12985996,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"29","issue":"1","first_page":"136","last_page":"137"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9987999796867371,"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":0.9987999796867371,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9898999929428101,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9703999757766724,"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/separable-space","display_name":"Separable space","score":0.4650944471359253},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.41726547479629517},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.41028547286987305},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3957775831222534},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36429110169410706},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.355021595954895},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35252952575683594},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30896449089050293},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.15011215209960938}],"concepts":[{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.4650944471359253},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.41726547479629517},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.41028547286987305},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3957775831222534},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36429110169410706},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.355021595954895},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35252952575683594},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30896449089050293},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.15011215209960938},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1983.1056616","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1983.1056616","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W1589291987","https://openalex.org/W1606480398"],"related_works":["https://openalex.org/W4321064619","https://openalex.org/W2009525028","https://openalex.org/W2023672523","https://openalex.org/W3011179836","https://openalex.org/W2962925412","https://openalex.org/W2483165346","https://openalex.org/W2053599029","https://openalex.org/W4297752497","https://openalex.org/W4301705099","https://openalex.org/W2980963558"],"abstract_inverted_index":{"Given":[0],"a":[1,8],"positive":[2],"integer":[3],"<tex":[4,11,15,29,37,47,51,63,71],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[5,12,16,30,38,48,52,64,72],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k</tex>":[6],"and":[7],"prime":[9],"power":[10],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">q</tex>":[13],"with":[14],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">q":[17],"\\leq":[18],"k</tex>":[19],",":[20],"it":[21],"is":[22,50,80],"proved":[23],"that":[24],"the":[25,59],"largest":[26,60],"value":[27,61],"of":[28,62],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</tex>":[31,65],"for":[32,58,66],"which":[33,67],"there":[34,68],"exists":[35,69],"an":[36,70],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">[n,k,n-k+l]</tex>":[39],"maximum":[40],"distance":[41],"separable":[42],"(MDS)":[43],"code":[44,75],"over":[45,76],"GF":[46],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">(q)</tex>":[49],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k+1</tex>":[53],".":[54],"A":[55],"simple":[56],"proof":[57],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">[n,2,n-1]</tex>":[73],"MDS":[74],"any":[77],"finite":[78],"field":[79],"also":[81],"given.":[82]},"counts_by_year":[{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
