{"id":"https://openalex.org/W7213934878","doi":"https://doi.org/10.48550/arxiv.2609.21395","title":"Exponentially Larger Deletion-Correcting Codes and Constant-List-Decodable Insertion-Deletion Codes","display_name":"Exponentially Larger Deletion-Correcting Codes and Constant-List-Decodable Insertion-Deletion Codes","publication_year":2026,"publication_date":"2026-09-18","ids":{"openalex":"https://openalex.org/W7213934878","doi":"https://doi.org/10.48550/arxiv.2609.21395"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.21395","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21395","pdf_url":"https://arxiv.org/pdf/2609.21395","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.21395","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083157397","display_name":"Han Mao Kiah","orcid":"https://orcid.org/0000-0001-5611-0848","observed_orcids":["https://orcid.org/0000-0001-5611-0848"]},"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":"Kiah, Han Mao","raw_affiliation_strings":["School of Physical and Mathematical Sciences , Nanyang Technological University , Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physical and Mathematical Sciences , Nanyang Technological University , Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061347472","display_name":"Hengjia Wei","orcid":"https://orcid.org/0000-0001-8136-1489","observed_orcids":["https://orcid.org/0000-0001-8136-1489"]},"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":"Wei, Hengjia","raw_affiliation_strings":["School of Physical and Mathematical Sciences , Nanyang Technological University , Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physical and Mathematical Sciences , Nanyang Technological University , Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5133764875","display_name":"Ruixiao Zeng","orcid":"https://orcid.org/0009-0006-7496-5528","observed_orcids":["https://orcid.org/0009-0006-7496-5528"]},"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":"Zeng, Ruixiao","raw_affiliation_strings":["School of Physical and Mathematical Sciences , Nanyang Technological University , Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physical and Mathematical Sciences , Nanyang Technological University , Singapore","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I172675005"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":0.9639000296592712,"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":0.9639000296592712,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.024900000542402267,"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/T11269","display_name":"Algorithms and Data Compression","score":0.008200000040233135,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/list-decoding","display_name":"list decoding","score":0.6790000200271606},{"id":"https://openalex.org/keywords/unique-decoding","display_name":"unique decoding","score":0.6800000071525574},{"id":"https://openalex.org/keywords/binary-codes","display_name":"binary codes","score":0.7020000219345093},{"id":"https://openalex.org/keywords/achievable-rate-bounds","display_name":"achievable rate bounds","score":0.5910000205039978},{"id":"https://openalex.org/keywords/runs","display_name":"runs","score":0.4050000011920929},{"id":"https://openalex.org/keywords/lovasz-local-lemma","display_name":"Lov\u00e1sz local lemma","score":0.9810000061988831},{"id":"https://openalex.org/keywords/supersequences","display_name":"supersequences","score":0.7639999985694885},{"id":"https://openalex.org/keywords/combinatorial-bounds","display_name":"combinatorial bounds","score":0.460999995470047}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.8176000118255615},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8033999800682068},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7807000279426575},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5435000061988831},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5126000046730042},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.4675000011920929},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.46639999747276306},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.4465000033378601},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.43059998750686646},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.40149998664855957},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.37130001187324524},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.37130001187324524},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.3675000071525574},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.3393000066280365},{"id":"https://openalex.org/C166530166","wikidata":"https://www.wikidata.org/wiki/Q1970635","display_name":"Hamming bound","level":5,"score":0.28850001096725464},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C41431624","wikidata":"https://www.wikidata.org/wiki/Q1053357","display_name":"Block size","level":3,"score":0.27649998664855957},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.2720000147819519},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.25060001015663147}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.21395","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21395","pdf_url":"https://arxiv.org/pdf/2609.21395","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.21395","doi":"https://doi.org/10.48550/arxiv.2609.21395","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.21395","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.21395","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21395","pdf_url":"https://arxiv.org/pdf/2609.21395","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2857663206","display_name":null,"funder_award_id":"12371523","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213934878.pdf","grobid_xml":"https://content.openalex.org/works/W7213934878.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4390650975","https://openalex.org/W7162416190","https://openalex.org/W2803538544","https://openalex.org/W3088092736","https://openalex.org/W2102799756","https://openalex.org/W2115151682","https://openalex.org/W2977214684","https://openalex.org/W2574559990","https://openalex.org/W7167587126","https://openalex.org/W7222914174"],"abstract_inverted_index":{"We":[0,85,129],"establish":[1,87],"improved":[2],"asymptotic":[3,148],"rate":[4,31],"bounds":[5,57,117,123],"for":[6,58,98,161],"adversarial":[7],"insertion--deletion":[8],"codes.":[9,63],"For":[10,43],"binary":[11,59],"unique-deletion":[12],"correction":[13],"in":[14],"the":[15,67,106,110,156],"linear-deletion":[16],"regime,":[17],"we":[18,53],"strictly":[19,154],"improve":[20],"Levenshtein's":[21],"classical":[22],"lower-bound":[23],"expression.":[24],"At":[25],"deletion":[26,60,102,121],"fraction":[27],"$\u03b4=0.1$,":[28],"our":[29],"achievable":[30],"increases":[32],"from":[33],"$0.162009$":[34],"to":[35,126],"$0.194890$,":[36],"a":[37,88,132,139],"relative":[38],"gain":[39],"of":[40,74,95,101],"approximately":[41],"$20.30\\%$.":[42],"list":[44,50,111],"decoding":[45],"with":[46,71],"any":[47],"prescribed":[48],"finite":[49],"size":[51],"$L$,":[52],"obtain":[54],"new":[55],"achievable-rate":[56],"and":[61,77,82,120,138,153,165],"insertion":[62,96,115,158],"Our":[64],"approach":[65],"combines":[66],"Lov\u00e1sz":[68],"local":[69],"lemma":[70],"refined":[72],"counting":[73],"common":[75],"subsequences":[76],"supersequences,":[78],"using":[79],"generating":[80],"functions":[81],"run-restricted":[83],"sampling.":[84],"also":[86,130],"combinatorial":[89],"reduction":[90],"that":[91],"trades":[92],"$L$":[93,164],"units":[94],"budget":[97,103],"one":[99],"unit":[100],"without":[104],"changing":[105],"code":[107],"or":[108],"increasing":[109],"size.":[112],"It":[113],"transfers":[114],"lower":[116],"at":[118,124,151],"$\u03b3+L\u03b4$":[119],"upper":[122,136,142,159],"$\u03b4+\u03b3/L$":[125],"mixed":[127],"errors.":[128],"derive":[131],"run-counting":[133],"Levenshtein-type":[134],"list-decoding":[135],"bound":[137,150,160],"higher-order":[140],"Elias-type":[141],"bound.":[143],"The":[144],"latter":[145],"recovers":[146],"Yasunaga's":[147],"unique-decoding":[149],"$L=1$":[152],"improves":[155],"Haeupler--Shahrasbi--Sudan":[157],"every":[162],"fixed":[163],"$0<\u03b3":[166]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-09-22T00:00:00"}
