{"id":"https://openalex.org/W7134228613","doi":"https://doi.org/10.48550/arxiv.2603.06489","title":"The DNA Coverage Depth Problem: Duality, Weight Distributions, and Applications","display_name":"The DNA Coverage Depth Problem: Duality, Weight Distributions, and Applications","publication_year":2026,"publication_date":"2026-03-06","ids":{"openalex":"https://openalex.org/W7134228613","doi":"https://doi.org/10.48550/arxiv.2603.06489"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2603.06489","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"article","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/A5120072585","display_name":"Matteo Bertuzzo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bertuzzo, Matteo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025356502","display_name":"Alberto Ravagnani","orcid":"https://orcid.org/0000-0001-5901-9484"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ravagnani, Alberto","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5021586372","display_name":"Eitan Yaakobi","orcid":"https://orcid.org/0000-0002-9851-5234"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yaakobi, Eitan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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":0.21036905,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T12029","display_name":"DNA and Biological Computing","score":0.9541000127792358,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9541000127792358,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10207","display_name":"Advanced biosensing and bioanalysis techniques","score":0.012799999676644802,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10432","display_name":"DNA and Nucleic Acid Chemistry","score":0.004399999976158142,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/generator-matrix","display_name":"Generator matrix","score":0.5781000256538391},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.571399986743927},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5532000064849854},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.5227000117301941},{"id":"https://openalex.org/keywords/ternary-operation","display_name":"Ternary operation","score":0.48739999532699585},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4740000069141388},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.3635999858379364}],"concepts":[{"id":"https://openalex.org/C1842014","wikidata":"https://www.wikidata.org/wiki/Q1502046","display_name":"Generator matrix","level":3,"score":0.5781000256538391},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.571399986743927},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5532000064849854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5273000001907349},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.5227000117301941},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.48739999532699585},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4740000069141388},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46790000796318054},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3815999925136566},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.3635999858379364},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.35740000009536743},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33000001311302185},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32839998602867126},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.31049999594688416},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.27630001306533813},{"id":"https://openalex.org/C63361517","wikidata":"https://www.wikidata.org/wiki/Q5645805","display_name":"Hamming weight","level":5,"score":0.26600000262260437},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.26499998569488525},{"id":"https://openalex.org/C164680029","wikidata":"https://www.wikidata.org/wiki/Q1055293","display_name":"Multiple","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C552990157","wikidata":"https://www.wikidata.org/wiki/Q7430","display_name":"DNA","level":2,"score":0.25279998779296875}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2603.06489","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2603.06489","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.06489","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,"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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2603.06489","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,118],"coverage":[1,80,129],"depth":[2,81,130],"problem":[3,82],"in":[4,135],"DNA":[5,79],"data":[6],"storage":[7],"is":[8,123],"about":[9],"computing":[10],"the":[11,33,78,92,106,128,138],"expected":[12,34],"number":[13,35],"of":[14,26,36,94,120,131,137,141],"reads":[15],"needed":[16],"to":[17,41,76],"recover":[18],"all":[19],"encoded":[20],"strands.":[21],"Given":[22],"a":[23,27,124,132],"generator":[24],"matrix":[25],"linear":[28,85,133],"code,":[29],"this":[30,70,121],"quantity":[31],"equals":[32],"randomly":[37],"drawn":[38],"columns":[39],"required":[40],"obtain":[42],"full":[43],"rank.":[44],"While":[45],"MDS":[46],"codes":[47],"are":[48],"optimal":[49],"when":[50],"they":[51],"exist,":[52],"i.e.,":[53],"over":[54,66],"large":[55],"fields,":[56],"practical":[57],"scenarios":[58],"may":[59],"rely":[60],"on":[61,88],"structured":[62],"code":[63,134],"families":[64],"defined":[65],"small":[67],"fields.":[68],"In":[69],"work,":[71],"we":[72,101],"develop":[73],"combinatorial":[74],"tools":[75],"solve":[77],"for":[83,105,127],"various":[84],"codes,":[86],"based":[87],"duality":[89],"arguments":[90],"and":[91,114],"notion":[93],"extended":[95,111],"weight":[96,139],"enumerator.":[97],"Using":[98],"these":[99],"methods,":[100],"derive":[102],"closed":[103],"formulas":[104],"simplex,":[107],"Hamming,":[108],"ternary":[109,112],"Golay,":[110,113],"first-order":[115],"Reed-Muller":[116],"codes.":[117],"centerpiece":[119],"paper":[122],"general":[125],"expression":[126],"terms":[136],"distributions":[140],"its":[142],"higher-field":[143],"extensions.":[144]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-03-10T00:00:00"}
