{"id":"https://openalex.org/W2069026918","doi":"https://doi.org/10.1109/tit.2012.2227110","title":"Zigzag Codes: MDS Array Codes With Optimal Rebuilding","display_name":"Zigzag Codes: MDS Array Codes With Optimal Rebuilding","publication_year":2012,"publication_date":"2012-11-21","ids":{"openalex":"https://openalex.org/W2069026918","doi":"https://doi.org/10.1109/tit.2012.2227110","mag":"2069026918"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2012.2227110","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2227110","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1112.0371","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Itzhak Tamo","orcid":null},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]},{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["IL","US"],"is_corresponding":true,"raw_author_name":"Itzhak Tamo","raw_affiliation_strings":["Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA","Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beersheva, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beersheva, Israel","institution_ids":["https://openalex.org/I124227911"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Zhiying Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhiying Wang","raw_affiliation_strings":["Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":null,"display_name":"Jehoshua Bruck","orcid":null},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jehoshua Bruck","raw_affiliation_strings":["Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I122411786","https://openalex.org/I124227911"],"apc_list":null,"apc_paid":null,"fwci":22.7241,"has_fulltext":false,"cited_by_count":303,"citation_normalized_percentile":{"value":0.99616503,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"59","issue":"3","first_page":"1597","last_page":"1616"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11181","display_name":"Advanced Data Storage Technologies","score":0.9735999703407288,"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"}},"topics":[{"id":"https://openalex.org/T11181","display_name":"Advanced Data Storage Technologies","score":0.9735999703407288,"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/T10772","display_name":"Distributed systems and fault tolerance","score":0.0071000000461936,"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/T11614","display_name":"Cloud Data Security Solutions","score":0.005499999970197678,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/erasure","display_name":"Erasure","score":0.6277999877929688},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.5475999712944031},{"id":"https://openalex.org/keywords/erasure-code","display_name":"Erasure code","score":0.5351999998092651},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.4869999885559082},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.4733000099658966},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4607999920845032},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4584999978542328},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.4056999981403351},{"id":"https://openalex.org/keywords/list-decoding","display_name":"List decoding","score":0.39320001006126404}],"concepts":[{"id":"https://openalex.org/C2778790127","wikidata":"https://www.wikidata.org/wiki/Q484885","display_name":"Erasure","level":2,"score":0.6277999877929688},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.5475999712944031},{"id":"https://openalex.org/C137529215","wikidata":"https://www.wikidata.org/wiki/Q5385031","display_name":"Erasure code","level":3,"score":0.5351999998092651},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5321999788284302},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.4869999885559082},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.4733000099658966},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4726000130176544},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4607999920845032},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4584999978542328},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4296000003814697},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41449999809265137},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4056999981403351},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.39320001006126404},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.3790999948978424},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3720000088214874},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.36169999837875366},{"id":"https://openalex.org/C103093684","wikidata":"https://www.wikidata.org/wiki/Q7094069","display_name":"Online codes","level":5,"score":0.36070001125335693},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.35910001397132874},{"id":"https://openalex.org/C192271897","wikidata":"https://www.wikidata.org/wiki/Q198438","display_name":"Zigzag","level":2,"score":0.34529998898506165},{"id":"https://openalex.org/C13021383","wikidata":"https://www.wikidata.org/wiki/Q1228738","display_name":"Disk array","level":2,"score":0.3382999897003174},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.2994999885559082},{"id":"https://openalex.org/C65058987","wikidata":"https://www.wikidata.org/wiki/Q7826005","display_name":"Tornado code","level":5,"score":0.28690001368522644},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C128151799","wikidata":"https://www.wikidata.org/wiki/Q13563306","display_name":"Luby transform code","level":5,"score":0.2709999978542328},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.26829999685287476},{"id":"https://openalex.org/C149862233","wikidata":"https://www.wikidata.org/wiki/Q864142","display_name":"Binary erasure channel","level":4,"score":0.2678000032901764},{"id":"https://openalex.org/C153207627","wikidata":"https://www.wikidata.org/wiki/Q863873","display_name":"Code word","level":3,"score":0.2671999931335449},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C47191418","wikidata":"https://www.wikidata.org/wiki/Q3510462","display_name":"Information-theoretic security","level":3,"score":0.2556999921798706},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.25220000743865967}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2012.2227110","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2227110","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:arXiv.org:1112.0371","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1112.0371","pdf_url":"https://arxiv.org/pdf/1112.0371","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":null,"raw_type":"text"},{"id":"pmh:oai:authors.library.caltech.edu:37585","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20130321-102330661","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1112.0371","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1112.0371","pdf_url":"https://arxiv.org/pdf/1112.0371","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1971493351","https://openalex.org/W1984324195","https://openalex.org/W2063292248","https://openalex.org/W2083480092","https://openalex.org/W2102047288","https://openalex.org/W2105185344","https://openalex.org/W2114708944","https://openalex.org/W2136583008","https://openalex.org/W2137291643","https://openalex.org/W2143174824","https://openalex.org/W2147323018","https://openalex.org/W2147343704","https://openalex.org/W2157451524","https://openalex.org/W2158646168","https://openalex.org/W2161104579","https://openalex.org/W2163775180","https://openalex.org/W2166011389","https://openalex.org/W2797315706","https://openalex.org/W2911280162","https://openalex.org/W2963178700","https://openalex.org/W6636645890"],"related_works":[],"abstract_inverted_index":{"Maximum":[0],"distance":[1],"separable":[2],"(MDS)":[3],"array":[4,222,245],"codes":[5,223,246],"are":[6],"widely":[7],"used":[8],"in":[9,24,42,128,237],"storage":[10],"systems":[11],"to":[12,39,44,126,130],"protect":[13],"data":[14],"against":[15],"erasures.":[16],"We":[17],"address":[18],"the":[19,25,31,34,47,55,60,72,79,83,91,98,103,118,139,162,183,194,238,254],"rebuilding":[20,73,140,195,227],"ratio":[21,74,141,196,228],"problem,":[22],"namely,":[23],"case":[26,88,184,239],"of":[27,33,57,63,93,102,121,185,213,229,240,275],"erasures,":[28],"what":[29],"is":[30,51,75,89,95,117,142,197],"fraction":[32],"remaining":[35,80],"information":[36,122],"that":[37,53,65,111,123,138,181,224],"needs":[38,125],"be":[40],"accessed":[41],"order":[43,129],"rebuild":[45],"exactly":[46],"lost":[48],"information?":[49],"It":[50],"clear":[52],"when":[54,90],"number":[56,62,92],"erasures":[58,64,94],"equals":[59],"maximum":[61],"an":[66,108,168,282],"MDS":[67,109,221],"code":[68,110],"can":[69,112],"correct,":[70],"then":[71],"1":[76],"(access":[77],"all":[78],"information).":[81],"However,":[82],"interesting":[84],"and":[85,152,179,250,262,278,281],"more":[86],"practical":[87],"smaller":[96],"than":[97],"erasure":[99,188],"correcting":[100,192,220],"capability":[101],"code.":[104],"For":[105],"example,":[106],"consider":[107],"correct":[113,131],"two":[114],"erasures:":[115],"What":[116],"smallest":[119],"amount":[120],"one":[124],"access":[127],"a":[132,186,190,210,241,272],"single":[133,187,242],"erasure?":[134],"Previous":[135],"work":[136],"showed":[137],"bounded":[143],"between":[144],"<formula":[145,153,198,214,230,256,263],"formulatype=\"inline\"":[146,154,199,215,231,257,264],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[147,155,200,216,232,258,265],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex":[148,156,201,217,233,259],"Notation=\"TeX\">${{1}":[149,202,234],"\\over":[150,158,203,235],"{2}}$</tex></formula>":[151,204],"Notation=\"TeX\">${{3}":[157],"{4}}$</tex></formula>":[159],";":[160],"however,":[161],"exact":[163],"value":[164],"was":[165],"left":[166],"as":[167],"open":[169,177],"problem.":[170],"In":[171,206],"this":[172,176],"paper,":[173],"we":[174,208],"solve":[175],"problem":[178],"prove":[180],"for":[182],"with":[189],"two-erasure":[191],"code,":[193],".":[205],"general,":[207],"construct":[209],"new":[211],"family":[212],"Notation=\"TeX\">$r$</tex></formula>":[218],"-erasure":[219],"has":[225],"optimal":[226,283],"{r}}$</tex></formula>":[236],"erasure.":[243],"Our":[244],"have":[247],"efficient":[248],"encoding":[249],"decoding":[251],"algorithms":[252],"(for":[253],"cases":[255],"Notation=\"TeX\">$r=2$</tex>":[260],"</formula>":[261],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[266],"<tex":[267],"Notation=\"TeX\">$r=3$</tex></formula>":[268],",":[269],"they":[270],"use":[271],"finite":[273],"field":[274],"size":[276],"3":[277],"4,":[279],"respectively)":[280],"update":[284],"property.":[285]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":20},{"year":2024,"cited_by_count":21},{"year":2023,"cited_by_count":21},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":22},{"year":2019,"cited_by_count":19},{"year":2018,"cited_by_count":25},{"year":2017,"cited_by_count":44},{"year":2016,"cited_by_count":37},{"year":2015,"cited_by_count":23},{"year":2014,"cited_by_count":28},{"year":2013,"cited_by_count":10}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2016-06-24T00:00:00"}
