{"id":"https://openalex.org/W7127949274","doi":"https://doi.org/10.48550/arxiv.2602.05462","title":"Explicit List-Decodable Linearized Reed-Solomon and Folded Linearized Reed-Solomon Subcodes","display_name":"Explicit List-Decodable Linearized Reed-Solomon and Folded Linearized Reed-Solomon Subcodes","publication_year":2026,"publication_date":"2026-02-05","ids":{"openalex":"https://openalex.org/W7127949274","doi":"https://doi.org/10.48550/arxiv.2602.05462"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.05462","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"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/A5093974036","display_name":"Kuo Shang","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Shang, Kuo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125208635","display_name":"Chen Yuan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuan, Chen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5125220671","display_name":"Ruiqi Zhu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhu, Ruiqi","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5093974036"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.7299000024795532,"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":0.7299000024795532,"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":0.07079999893903732,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.025800000876188278,"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/metric","display_name":"Metric (unit)","score":0.7125999927520752},{"id":"https://openalex.org/keywords/list-decoding","display_name":"List decoding","score":0.7095999717712402},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.6642000079154968},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5120000243186951},{"id":"https://openalex.org/keywords/hamming-bound","display_name":"Hamming bound","score":0.46219998598098755},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.4596000015735626},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.4047999978065491},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.38679999113082886},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.3781000077724457}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7533000111579895},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.7125999927520752},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.7095999717712402},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.6642000079154968},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5120000243186951},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46709999442100525},{"id":"https://openalex.org/C166530166","wikidata":"https://www.wikidata.org/wiki/Q1970635","display_name":"Hamming bound","level":5,"score":0.46219998598098755},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4596000015735626},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.4047999978065491},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.38679999113082886},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.3781000077724457},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.3752000033855438},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.37139999866485596},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.35929998755455017},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.3463999927043915},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.34610000252723694},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.33160001039505005},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.32010000944137573},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.30889999866485596},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3073999881744385},{"id":"https://openalex.org/C193969084","wikidata":"https://www.wikidata.org/wiki/Q7452500","display_name":"Sequential decoding","level":4,"score":0.2888000011444092},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.25679999589920044},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.05462","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.05462","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.05462","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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.05462","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,12],"sum-rank":[1,13,35,58,80,200,226],"metric":[2,14,59,81,201],"is":[3,116],"the":[4,7,34,79,112,121,149,165,170,182,186,194,209,225],"mixture":[5],"of":[6,37,56,76,96,164,188,198],"Hamming":[8],"and":[9,26,40,45,90,111,147,168],"rank":[10],"metrics.":[11],"found":[15],"its":[16],"application":[17],"in":[18,78],"network":[19],"coding,":[20,25],"locally":[21],"repairable":[22],"codes,":[23,98],"space-time":[24],"quantum-resistant":[27],"cryptography.":[28],"Linearized":[29,134],"Reed-Solomon":[30,38,44,135],"(LRS)":[31],"codes":[32,39,60,93,202,223],"are":[33,94,177],"analogue":[36],"strictly":[41],"generalize":[42],"both":[43],"Gabidulin":[46],"codes.":[47,137],"In":[48],"this":[49,191],"work,":[50],"we":[51,125],"construct":[52],"an":[53,105],"explicit":[54,172,196],"family":[55],"$\\mathbb{F}_h$-linear":[57],"over":[61],"arbitrary":[62],"fields":[63],"$\\mathbb{F}_h$.":[64],"Our":[65,92],"construction":[66,197],"enables":[67,161],"efficient":[68,205],"list":[69,114,166,179,206],"decoding":[70,113,130,207,211],"up":[71],"to":[72,104,132],"a":[73,154,215],"fraction":[74],"$\u03c1$":[75],"errors":[77],"with":[82],"rate":[83],"$1-\u03c1-\\varepsilon$,":[84],"for":[85,219],"any":[86],"desired":[87],"$\u03c1\\in":[88],"(0,1)$":[89],"$\\varepsilon&gt;0$.":[91],"subcodes":[95,175],"LRS":[97,123],"obtained":[99],"by":[100,118],"restricting":[101],"message":[102],"polynomials":[103],"$\\mathbb{F}_h$-subspace":[106],"derived":[107],"from":[108],"subspace":[109],"designs,":[110],"size":[115,167],"bounded":[117],"$h^{\\mathrm{poly}(1/\\varepsilon)}$.":[119],"Beyond":[120],"standard":[122],"setting,":[124],"further":[126],"extend":[127],"our":[128,189],"linear-algebraic":[129],"framework":[131,218],"folded":[133,141],"(FLRS)":[136],"We":[138],"show":[139],"that":[140,148,176,203],"evaluations":[142],"satisfy":[143],"appropriate":[144],"interpolation":[145],"conditions":[146],"corresponding":[150],"solution":[151],"space":[152],"forms":[153],"low-dimensional,":[155],"structured":[156],"affine":[157],"subspace.":[158],"This":[159],"structure":[160],"effective":[162],"control":[163],"yields":[169],"first":[171,195],"positive-rate":[173,199],"FLRS":[174],"efficiently":[178,221],"decodable":[180,222],"beyond":[181,208],"unique-decoding":[183],"radius.":[184],"To":[185],"best":[187],"knowledge,":[190],"also":[192],"constitutes":[193],"admit":[204],"unique":[210],"radius,":[212],"thereby":[213],"providing":[214],"new":[216],"general":[217],"constructing":[220],"under":[224],"metric.":[227]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-02-07T00:00:00"}
