{"id":"https://openalex.org/W3107393399","doi":"https://doi.org/10.1137/20m1386001","title":"A General Family of MSRD Codes and PMDS Codes with Smaller Field Sizes from Extended Moore Matrices","display_name":"A General Family of MSRD Codes and PMDS Codes with Smaller Field Sizes from Extended Moore Matrices","publication_year":2022,"publication_date":"2022-08-16","ids":{"openalex":"https://openalex.org/W3107393399","doi":"https://doi.org/10.1137/20m1386001","mag":"3107393399"},"language":"en","primary_location":{"id":"doi:10.1137/20m1386001","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1386001","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2011.14109","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006688702","display_name":"Umberto Mart\u00ednez-Pe\u00f1as","orcid":"https://orcid.org/0000-0003-2626-8139"},"institutions":[{"id":"https://openalex.org/I57825437","display_name":"University of Neuch\u00e2tel","ror":"https://ror.org/00vasag41","country_code":"CH","type":"education","lineage":["https://openalex.org/I57825437"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Umberto Mart\u00cdnez-Pen\u0342as","raw_affiliation_strings":["University of Neuch\u00e2tel"],"raw_orcid":"https://orcid.org/0000-0003-2626-8139","affiliations":[{"raw_affiliation_string":"University of Neuch\u00e2tel","institution_ids":["https://openalex.org/I57825437"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5006688702"],"corresponding_institution_ids":["https://openalex.org/I57825437"],"apc_list":null,"apc_paid":null,"fwci":0.5549,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.7043792,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"36","issue":"3","first_page":"1868","last_page":"1886"},"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9976999759674072,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9958999752998352,"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/linear-code","display_name":"Linear code","score":0.7823532819747925},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.7088795900344849},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6532027125358582},{"id":"https://openalex.org/keywords/generator-matrix","display_name":"Generator matrix","score":0.5741303563117981},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.5065311193466187},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4920296370983124},{"id":"https://openalex.org/keywords/conjugacy-class","display_name":"Conjugacy class","score":0.45301535725593567},{"id":"https://openalex.org/keywords/hamming-bound","display_name":"Hamming bound","score":0.45067504048347473},{"id":"https://openalex.org/keywords/polynomial-code","display_name":"Polynomial code","score":0.4462088346481323},{"id":"https://openalex.org/keywords/reed\u2013muller-code","display_name":"Reed\u2013Muller code","score":0.44073817133903503},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.4304192364215851},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3977700471878052},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19198042154312134},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.12811636924743652}],"concepts":[{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.7823532819747925},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.7088795900344849},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6532027125358582},{"id":"https://openalex.org/C1842014","wikidata":"https://www.wikidata.org/wiki/Q1502046","display_name":"Generator matrix","level":3,"score":0.5741303563117981},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.5065311193466187},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4920296370983124},{"id":"https://openalex.org/C87945829","wikidata":"https://www.wikidata.org/wiki/Q1353233","display_name":"Conjugacy class","level":2,"score":0.45301535725593567},{"id":"https://openalex.org/C166530166","wikidata":"https://www.wikidata.org/wiki/Q1970635","display_name":"Hamming bound","level":5,"score":0.45067504048347473},{"id":"https://openalex.org/C39635130","wikidata":"https://www.wikidata.org/wiki/Q7226636","display_name":"Polynomial code","level":5,"score":0.4462088346481323},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.44073817133903503},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.4304192364215851},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3977700471878052},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19198042154312134},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.12811636924743652}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1386001","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1386001","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2011.14109","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.14109","pdf_url":"https://arxiv.org/pdf/2011.14109","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},{"id":"mag:3107393399","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2011.14109.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2011.14109","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2011.14109","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2011.14109","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.14109","pdf_url":"https://arxiv.org/pdf/2011.14109","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3107393399.pdf","grobid_xml":"https://content.openalex.org/works/W3107393399.grobid-xml"},"referenced_works_count":54,"referenced_works":["https://openalex.org/W1557415002","https://openalex.org/W1559343931","https://openalex.org/W1606480398","https://openalex.org/W1966237841","https://openalex.org/W1980073965","https://openalex.org/W1993359877","https://openalex.org/W1993830711","https://openalex.org/W1996118782","https://openalex.org/W1998725765","https://openalex.org/W2004166394","https://openalex.org/W2021537862","https://openalex.org/W2031876696","https://openalex.org/W2050687505","https://openalex.org/W2060646539","https://openalex.org/W2069554151","https://openalex.org/W2095547380","https://openalex.org/W2095980332","https://openalex.org/W2108550051","https://openalex.org/W2124961791","https://openalex.org/W2126824576","https://openalex.org/W2148575324","https://openalex.org/W2333324284","https://openalex.org/W2541979517","https://openalex.org/W2555108336","https://openalex.org/W2766426326","https://openalex.org/W2801400867","https://openalex.org/W2887564199","https://openalex.org/W2905846917","https://openalex.org/W2908383142","https://openalex.org/W2956089011","https://openalex.org/W2963073980","https://openalex.org/W2964326991","https://openalex.org/W2964892028","https://openalex.org/W2968589674","https://openalex.org/W2969716815","https://openalex.org/W2975679388","https://openalex.org/W2978757494","https://openalex.org/W2995134452","https://openalex.org/W3045565582","https://openalex.org/W3081293222","https://openalex.org/W3084159079","https://openalex.org/W3092542508","https://openalex.org/W3104978253","https://openalex.org/W3110284774","https://openalex.org/W3136350169","https://openalex.org/W3155530075","https://openalex.org/W3165931569","https://openalex.org/W3172479183","https://openalex.org/W3178595420","https://openalex.org/W3196309825","https://openalex.org/W3206422952","https://openalex.org/W4205979625","https://openalex.org/W4206775542","https://openalex.org/W4213145874"],"related_works":["https://openalex.org/W3155530075","https://openalex.org/W3016740036","https://openalex.org/W2956089011","https://openalex.org/W2144461322","https://openalex.org/W3200793038","https://openalex.org/W2253768740","https://openalex.org/W2111721896","https://openalex.org/W2169117254","https://openalex.org/W2101377553","https://openalex.org/W2013746945","https://openalex.org/W1985458810","https://openalex.org/W2950506350","https://openalex.org/W1664162612","https://openalex.org/W3165931569","https://openalex.org/W1554098076","https://openalex.org/W2085788417","https://openalex.org/W2743327613","https://openalex.org/W2105194937","https://openalex.org/W2079696964","https://openalex.org/W1543977106"],"abstract_inverted_index":{"We":[0,86],"construct":[1],"six":[2,98],"new":[3,42,99],"explicit":[4,43],"families":[5,44,100],"of":[6,14,36,45,81,101,129],"linear":[7,46,83,102],"maximum":[8,48],"sum-rank":[9,131],"distance":[10,49,132],"(MSRD)":[11],"codes,":[12,113,115,117,128],"each":[13],"which":[15],"has":[16],"the":[17,37,78],"smallest":[18],"field":[19,55,107],"sizes":[20,56,108],"among":[21],"all":[22],"known":[23],"MSRD":[24,84,103,123],"codes":[25,52,60,92,104,124],"for":[26,61],"some":[27,62],"parameter":[28,63],"regime.":[29],"Using":[30],"them":[31],"and":[32,118,141],"a":[33,82,135],"previous":[34,58],"result":[35],"author,":[38],"we":[39],"provide":[40],"two":[41],"partial":[47],"separable":[50],"(PMDS)":[51],"with":[53,93,105],"smaller":[54,106],"than":[57],"PMDS":[59],"regimes.":[64],"Our":[65],"approach":[66],"is":[67],"to":[68],"characterize":[69],"evaluation":[70],"points":[71],"that":[72],"turn":[73],"extended":[74],"Moore":[75],"matrices":[76],"into":[77],"parity-check":[79],"matrix":[80],"code.":[85],"then":[87],"produce":[88],"such":[89],"sequences":[90],"from":[91],"good":[94],"Hamming-metric":[95],"parameters.":[96],"The":[97,122],"are":[109],"obtained":[110],"using":[111],"MDS":[112],"Hamming":[114,127],"Bose--Chaudhuri--Hocquenghem":[116],"three":[119],"algebraic-geometry":[120],"codes.":[121],"based":[125],"on":[126],"minimum":[130],"3,":[133],"meet":[134],"recent":[136],"bound":[137],"by":[138],"Byrne,":[139],"Gluesing-Luerssen,":[140],"Ravagnani":[142],"[IEEE":[143],"Trans.":[144],"Inform.":[145],"Theory,":[146],"67":[147],"(2021),":[148],"pp.":[149],"6456--6475].":[150]},"counts_by_year":[{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}