{"id":"https://openalex.org/W3172953899","doi":"https://doi.org/10.1109/tit.2022.3152398","title":"Multiple Criss-Cross Insertion and Deletion Correcting Codes","display_name":"Multiple Criss-Cross Insertion and Deletion Correcting Codes","publication_year":2022,"publication_date":"2022-02-16","ids":{"openalex":"https://openalex.org/W3172953899","doi":"https://doi.org/10.1109/tit.2022.3152398","mag":"3172953899"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2022.3152398","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3152398","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/A5034799688","display_name":"Lorenz Welter","orcid":"https://orcid.org/0000-0002-5135-6731"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Lorenz Welter","raw_affiliation_strings":["Institute for Communications Engineering, Technical University of Munich (TUM), Munich, Germany"],"raw_orcid":"https://orcid.org/0000-0002-5135-6731","affiliations":[{"raw_affiliation_string":"Institute for Communications Engineering, Technical University of Munich (TUM), Munich, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024768934","display_name":"Rawad Bitar","orcid":"https://orcid.org/0000-0002-4421-1024"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Rawad Bitar","raw_affiliation_strings":["Institute for Communications Engineering, Technical University of Munich (TUM), Munich, Germany"],"raw_orcid":"https://orcid.org/0000-0002-4421-1024","affiliations":[{"raw_affiliation_string":"Institute for Communications Engineering, Technical University of Munich (TUM), Munich, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041962883","display_name":"Antonia Wachter-Zeh","orcid":"https://orcid.org/0000-0002-5174-1947"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Antonia Wachter-Zeh","raw_affiliation_strings":["Institute for Communications Engineering, Technical University of Munich (TUM), Munich, Germany"],"raw_orcid":"https://orcid.org/0000-0002-5174-1947","affiliations":[{"raw_affiliation_string":"Institute for Communications Engineering, Technical University of Munich (TUM), Munich, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021586372","display_name":"Eitan Yaakobi","orcid":"https://orcid.org/0000-0002-9851-5234"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Eitan Yaakobi","raw_affiliation_strings":["Computer Science Department, Technion—Israel Institute of Technology, Haifa, Israel"],"raw_orcid":"https://orcid.org/0000-0002-9851-5234","affiliations":[{"raw_affiliation_string":"Computer Science Department, Technion—Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4702,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.5574774,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"68","issue":"6","first_page":"3767","last_page":"3779"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9997000098228455,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/notation","display_name":"Notation","score":0.705049991607666},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44350603222846985},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.406083881855011},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3609326481819153},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32244473695755005},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.16400140523910522}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.705049991607666},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44350603222846985},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.406083881855011},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3609326481819153},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32244473695755005},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.16400140523910522}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2022.3152398","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3152398","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"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1696196","is_oa":false,"landing_page_url":"https://mediatum.ub.tum.de/1696196","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"contributionToPeriodical"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1516293512","display_name":null,"funder_award_id":"291763","funder_id":"https://openalex.org/F4320333065","funder_display_name":"Seventh Framework Programme"},{"id":"https://openalex.org/G6645313866","display_name":null,"funder_award_id":"801434","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320333065","display_name":"Seventh Framework Programme","ror":null},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1647671624","https://openalex.org/W1941245335","https://openalex.org/W1993359877","https://openalex.org/W2057174629","https://openalex.org/W2097938859","https://openalex.org/W2101398931","https://openalex.org/W2110027055","https://openalex.org/W2133470506","https://openalex.org/W2137445826","https://openalex.org/W2172132228","https://openalex.org/W2317556569","https://openalex.org/W2541808997","https://openalex.org/W2555411750","https://openalex.org/W2567974234","https://openalex.org/W2584151571","https://openalex.org/W2751518651","https://openalex.org/W2897671136","https://openalex.org/W2962809499","https://openalex.org/W2963044831","https://openalex.org/W2963183421","https://openalex.org/W2964230863","https://openalex.org/W2979059622","https://openalex.org/W2982705741","https://openalex.org/W3020884051","https://openalex.org/W3080550366","https://openalex.org/W3092309105","https://openalex.org/W3100438601","https://openalex.org/W3100895107","https://openalex.org/W3113522538","https://openalex.org/W3136232502","https://openalex.org/W3161217554","https://openalex.org/W3165181323","https://openalex.org/W3196815013","https://openalex.org/W3197221533","https://openalex.org/W3199904058","https://openalex.org/W3203581880","https://openalex.org/W6636915900","https://openalex.org/W6776229821","https://openalex.org/W6791943875"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W1978225469","https://openalex.org/W2799759016","https://openalex.org/W3104631496","https://openalex.org/W4288772858","https://openalex.org/W2049729887","https://openalex.org/W2076027639","https://openalex.org/W2000144448","https://openalex.org/W1421410134","https://openalex.org/W1970195683"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"the":[3,18,98,115,118,125,138],"problem":[4,127,132],"of":[5,76,97,117],"correcting":[6,79,105],"multiple":[7],"criss-cross":[8],"insertions":[9,51],"and":[10,52,107,121],"deletions":[11,34,49],"in":[12],"arrays.":[13],"More":[14],"precisely,":[15],"we":[16,71],"study":[17],"unique":[19],"recovery":[20],"of$n":[21],"\\times":[22],"n$arrays":[23],"affected":[24],"by${t}$-criss-cross":[25],"deletionsdefined":[26],"as":[27],"any":[28],"combination":[29],"of${t_{\\mathrm":[30],"{r}}}$row":[31],"and${t_{\\mathrm":[32],"{c}}}$column":[33],"such":[35],"that${t_{\\mathrm":[36],"{r}}}+":[37],"{t_{\\mathrm":[38],"{c}}}=":[39],"{t}$for":[40],"a":[41,55,129],"given$t$.":[42],"We":[43],"show":[44,53],"an":[45,73],"equivalence":[46],"between":[47],"correcting${t}$-criss-cross":[48,57],"and${t}$-criss-cross":[50],"that":[54],"code":[56,80,100],"insertions/deletions":[58],"has":[59],"redundancy":[60,82],"at":[61],"least${t}":[62],"n":[63,66,87],"+":[64,88],"{t}\\log":[65],"-":[67],"\\log":[68,91],"({t}!)$.":[69],"Then,":[70],"present":[72],"existential":[74],"construction":[75,101],"a${t}$-criss-cross":[77],"insertion/deletion":[78],"with":[81],"bounded":[83],"from":[84],"above":[85],"by${t}":[86],"\\mathcal":[89],"{O}({t}^{2}":[90],"^{2}":[92],"n)$.":[93],"The":[94,110],"main":[95],"ingredients":[96],"presented":[99],"are":[102],"systematic":[103],"binary${t}$-deletion":[104],"codes":[106],"Gabidulin":[108],"codes.":[109],"first":[111],"ingredient":[112],"helps":[113],"locating":[114],"indices":[116],"inserted/deleted":[119],"rows":[120],"columns,":[122],"thus":[123],"transforming":[124],"insertion/deletion-correction":[126],"into":[128],"row/column":[130],"erasure-correction":[131],"which":[133],"is":[134],"then":[135],"solved":[136],"using":[137],"second":[139],"ingredient.":[140]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":2}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}