{"id":"https://openalex.org/W4399785204","doi":"https://doi.org/10.3934/amc.2024026","title":"On the matrix code of quadratic relationships for a Goppa code","display_name":"On the matrix code of quadratic relationships for a Goppa code","publication_year":2024,"publication_date":"2024-06-18","ids":{"openalex":"https://openalex.org/W4399785204","doi":"https://doi.org/10.3934/amc.2024026"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2024026","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2024026","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/amc.2024026","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010936130","display_name":"Rocco Mora","orcid":"https://orcid.org/0000-0001-5165-5320"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Rocco Mora","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010936130"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3637,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.63825988,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"19","issue":"3","first_page":"829","last_page":"852"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9905999898910522,"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"}},{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.9872000217437744,"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/mathematics","display_name":"Mathematics","score":0.9102942943572998},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6475337743759155},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.6458110809326172},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5599981546401978},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3997109532356262},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39850497245788574},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38776662945747375},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.10757699608802795},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07011380791664124},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05226048827171326}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9102942943572998},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6475337743759155},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.6458110809326172},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5599981546401978},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3997109532356262},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39850497245788574},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38776662945747375},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.10757699608802795},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07011380791664124},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05226048827171326},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2024026","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2024026","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/amc.2024026","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2024026","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1990361074","https://openalex.org/W1997772212","https://openalex.org/W2099250555","https://openalex.org/W2113494858","https://openalex.org/W2119117325","https://openalex.org/W2136772235","https://openalex.org/W3215246204","https://openalex.org/W4232836212","https://openalex.org/W4389104608"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2980963558","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W1976691234","https://openalex.org/W3212023493","https://openalex.org/W2090715877","https://openalex.org/W2572370460"],"abstract_inverted_index":{"In":[0],"this":[1,42],"article,":[2],"we":[3,44],"continue":[4],"the":[5,11,30,47,54,67,81,84,93,122,125],"analysis":[6],"started":[7],"in":[8,29,53,66,80,98,112],"[8]":[9,99],"for":[10,141],"matrix":[12,31,55],"code":[13,32],"of":[14,49,124,151,158],"quadratic":[15],"relationships":[16],"associated":[17,57],"with":[18,58],"a":[19,102,114,137,148,156],"Goppa":[20,61,85,143,161],"code.":[21],"We":[22,90,134],"provide":[23,136],"new":[24],"sparse":[25],"and":[26,33,153,160],"low-rank":[27],"elements":[28],"categorize":[34],"them":[35],"according":[36],"to":[37,41,100,120,146],"their":[38,130],"shape.":[39],"Thanks":[40],"description,":[43],"prove":[45],"that":[46],"set":[48],"rank":[50],"2":[51],"matrices":[52],"codes":[56],"square-free":[59],"binary":[60],"codes,":[62],"i.e.":[63],"those":[64],"used":[65],"Classic":[68],"McEiece":[69],"cryptosystem,":[70,127],"is":[71,76,88],"much":[72],"larger":[73],"than":[74],"what":[75],"expected,":[77],"at":[78],"least":[79],"case":[82],"where":[83],"polynomial":[86,144],"degree":[87],"2.":[89],"build":[91],"upon":[92],"algebraic":[94],"determinantal":[95],"modeling":[96],"introduced":[97],"derive":[101],"structural":[103],"attack":[104],"on":[105],"these":[106],"instances.":[107],"Our":[108],"method":[109],"can":[110],"break":[111],"just":[113],"few":[115],"seconds":[116],"some":[117],"recent":[118],"challenges":[119],"recover":[121],"key":[123],"McEliece":[126],"consistently":[128],"reducing":[129],"estimated":[131],"security":[132],"level.":[133],"also":[135],"general":[138],"method,":[139],"valid":[140],"any":[142],"degree,":[145],"transform":[147],"generic":[149],"pair":[150,157],"support":[152,159],"multiplier":[154],"into":[155],"polynomial.":[162]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2025-12-19T19:40:27.379048","created_date":"2025-10-10T00:00:00"}
