{"id":"https://openalex.org/W3000368444","doi":"https://doi.org/10.1109/isit44484.2020.9174384","title":"Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power","display_name":"Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power","publication_year":2020,"publication_date":"2020-06-01","ids":{"openalex":"https://openalex.org/W3000368444","doi":"https://doi.org/10.1109/isit44484.2020.9174384","mag":"3000368444"},"language":"en","primary_location":{"id":"doi:10.1109/isit44484.2020.9174384","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit44484.2020.9174384","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2001.04800","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090817394","display_name":"Julian Renner","orcid":"https://orcid.org/0000-0003-0584-2226"},"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":true,"raw_author_name":"Julian Renner","raw_affiliation_strings":["Technical University of Munich (TUM),Institute for Communications Engineering,Germany","Technical University of Munich"],"affiliations":[{"raw_affiliation_string":"Technical University of Munich (TUM),Institute for Communications Engineering,Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Technical University of Munich","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009036826","display_name":"Sven Puchinger","orcid":"https://orcid.org/0000-0002-7474-2678"},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Sven Puchinger","raw_affiliation_strings":["Technical University of Denmark (DTU),Department of Applied Mathematics and Computer Science,Denmark","Technical University of Denmark"],"affiliations":[{"raw_affiliation_string":"Technical University of Denmark (DTU),Department of Applied Mathematics and Computer Science,Denmark","institution_ids":["https://openalex.org/I96673099"]},{"raw_affiliation_string":"Technical University of Denmark","institution_ids":["https://openalex.org/I96673099"]}]},{"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":["Technical University of Munich (TUM),Institute for Communications Engineering,Germany","Technical University of Munich"],"affiliations":[{"raw_affiliation_string":"Technical University of Munich (TUM),Institute for Communications Engineering,Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Technical University of Munich","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035260653","display_name":"Camilla Hollanti","orcid":"https://orcid.org/0000-0001-5356-8669"},"institutions":[{"id":"https://openalex.org/I4210134318","display_name":"University of Technology","ror":"https://ror.org/03gbw6p94","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210134318"]},{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI","RU"],"is_corresponding":false,"raw_author_name":"Camilla Hollanti","raw_affiliation_strings":["Aalto University,Department of Mathematics and Systems Analysis,Finland","(Helsinki University of Technology)"],"affiliations":[{"raw_affiliation_string":"Aalto University,Department of Mathematics and Systems Analysis,Finland","institution_ids":["https://openalex.org/I9927081"]},{"raw_affiliation_string":"(Helsinki University of Technology)","institution_ids":["https://openalex.org/I4210134318"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079294052","display_name":"Ragnar Freij-Hollanti","orcid":"https://orcid.org/0000-0001-8156-2053"},"institutions":[{"id":"https://openalex.org/I4210134318","display_name":"University of Technology","ror":"https://ror.org/03gbw6p94","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210134318"]},{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI","RU"],"is_corresponding":false,"raw_author_name":"Ragnar Freij-Hollanti","raw_affiliation_strings":["Aalto University,Department of Mathematics and Systems Analysis,Finland","(Helsinki University of Technology)"],"affiliations":[{"raw_affiliation_string":"Aalto University,Department of Mathematics and Systems Analysis,Finland","institution_ids":["https://openalex.org/I9927081"]},{"raw_affiliation_string":"(Helsinki University of Technology)","institution_ids":["https://openalex.org/I4210134318"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5090817394"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":null,"apc_paid":null,"fwci":0.1371,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.52245109,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"19","last_page":"24"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9945999979972839,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9905999898910522,"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/mathematics","display_name":"Mathematics","score":0.6783962249755859},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5701289176940918},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.5650418996810913},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.5244094133377075},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.48060914874076843},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.47565290331840515},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.45582517981529236},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.45473793148994446},{"id":"https://openalex.org/keywords/prime-power","display_name":"Prime power","score":0.4525061547756195},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.425395667552948},{"id":"https://openalex.org/keywords/parity","display_name":"Parity (physics)","score":0.4224913716316223},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.41119861602783203},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.3911218047142029},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.3735876679420471},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15701699256896973}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6783962249755859},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5701289176940918},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.5650418996810913},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.5244094133377075},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.48060914874076843},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.47565290331840515},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45582517981529236},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.45473793148994446},{"id":"https://openalex.org/C174072685","wikidata":"https://www.wikidata.org/wiki/Q1667469","display_name":"Prime power","level":3,"score":0.4525061547756195},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.425395667552948},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.4224913716316223},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.41119861602783203},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.3911218047142029},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.3735876679420471},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15701699256896973},{"id":"https://openalex.org/C109214941","wikidata":"https://www.wikidata.org/wiki/Q18334","display_name":"Particle physics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1109/isit44484.2020.9174384","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit44484.2020.9174384","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2001.04800","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.04800","pdf_url":"https://arxiv.org/pdf/2001.04800","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":"mag:3000368444","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2001.04800","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:mediatum.ub.tum.de:node/1542784","is_oa":true,"landing_page_url":"http://mediatum.ub.tum.de/node?id=1542784","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:oai:pure.atira.dk:publications/b7dc4038-9653-44ff-b4e3-13fcfa4d4dce","is_oa":true,"landing_page_url":"https://orbit.dtu.dk/en/publications/b7dc4038-9653-44ff-b4e3-13fcfa4d4dce","pdf_url":null,"source":{"id":"https://openalex.org/S4306400705","display_name":"Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I96673099","host_organization_name":"Technical University of Denmark","host_organization_lineage":["https://openalex.org/I96673099"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Renner , J , Puchinger , S , Wachter-Zeh , A , Hollanti , C &amp; Freij-Hollanti , R 2020 , Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power . in Proceedings of 2020 IEEE International Symposium on Information Theory . , 9174384 , IEEE , IEEE International Symposium on Information Theory - Proceedings , vol. 2020-June , pp. 19-24 , 2020 IEEE International Symposium on Information Theory , Los Angeles , California , United States , 21/06/2020 . https://doi.org/10.1109/ISIT44484.2020.9174384","raw_type":"contributionToPeriodical"},{"id":"doi:10.48550/arxiv.2001.04800","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2001.04800","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:oai:arXiv.org:2001.04800","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.04800","pdf_url":"https://arxiv.org/pdf/2001.04800","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":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3000368444.pdf"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1993359877","https://openalex.org/W2095547380","https://openalex.org/W2278805587","https://openalex.org/W2569686998","https://openalex.org/W2807945672","https://openalex.org/W2936293964","https://openalex.org/W2964936392","https://openalex.org/W2967670694","https://openalex.org/W3006860762","https://openalex.org/W4205456245","https://openalex.org/W6694889516"],"related_works":["https://openalex.org/W3112682786","https://openalex.org/W2743327613","https://openalex.org/W1511991703","https://openalex.org/W1572783864","https://openalex.org/W3165931569","https://openalex.org/W2991133842","https://openalex.org/W2171294544","https://openalex.org/W1522276718","https://openalex.org/W2026698357","https://openalex.org/W2068593329","https://openalex.org/W2008006294","https://openalex.org/W1543977106","https://openalex.org/W2169117254","https://openalex.org/W1554098076","https://openalex.org/W2013746945","https://openalex.org/W2885726234","https://openalex.org/W2040618267","https://openalex.org/W2013369084","https://openalex.org/W1792388367","https://openalex.org/W2000812559"],"abstract_inverted_index":{"We":[0,82],"define":[1],"and":[2,26,79],"analyze":[3],"low-rank":[4],"parity-check":[5],"(LRPC)":[6],"codes":[7,33,68,78],"over":[8,43,69],"extension":[9],"rings":[10,53,73],"of":[11,102],"the":[12,99,103,117],"finite":[13,44,52,70],"chain":[14],"ring":[15],"Z":[16],"<sub":[17],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[18],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">pr</sub>":[19],",":[20],"where":[21],"p":[22],"is":[23,28,54,108,114],"a":[24,29,57,84],"prime":[25],"r":[27],"positive":[30],"integer.":[31],"LRPC":[32],"have":[34],"originally":[35],"been":[36],"proposed":[37],"by":[38,56,60],"Gaborit":[39],"et":[40,62],"al.":[41,63],"(2013)":[42],"fields":[45],"for":[46,110],"cryptographic":[47],"applications.":[48],"The":[49,105],"adaption":[50],"to":[51,76,116],"inspired":[55],"recent":[58],"paper":[59],"Kamche":[61],"(2019),":[64],"which":[65],"constructed":[66],"Gabidulin":[67],"principle":[71],"ideal":[72],"with":[74],"applications":[75],"space-time":[77],"network":[80],"coding.":[81],"give":[83],"decoding":[85],"algorithm":[86],"based":[87],"on":[88,98],"simple":[89],"linear-algebraic":[90],"operations.":[91],"Further,":[92],"we":[93],"derive":[94],"an":[95],"upper":[96,106],"bound":[97,107],"failure":[100],"probability":[101],"decoder.":[104],"valid":[109],"errors":[111],"whose":[112],"rank":[113],"equal":[115],"free":[118],"rank.":[119]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-21T08:13:44.787528","created_date":"2022-07-18T00:00:00"}