{"id":"https://openalex.org/W7116938686","doi":"https://doi.org/10.48550/arxiv.2512.17256","title":"Quasi-recursive MDS Matrices over Galois Rings","display_name":"Quasi-recursive MDS Matrices over Galois Rings","publication_year":2025,"publication_date":"2025-12-19","ids":{"openalex":"https://openalex.org/W7116938686","doi":"https://doi.org/10.48550/arxiv.2512.17256"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2512.17256","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.17256","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2512.17256","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5121068691","display_name":"Shakir Ali","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ali, Shakir","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049889442","display_name":"Atif Ahmad Khan","orcid":"https://orcid.org/0009-0009-2371-5707"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Khan, Atif Ahmad","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047180976","display_name":"Abhishek Kesarwani","orcid":"https://orcid.org/0000-0001-8488-6811"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kesarwani, Abhishek","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5056260755","display_name":"Susanta Kumar Samanta","orcid":"https://orcid.org/0000-0003-4643-5117"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Samanta, Susanta","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5121068691"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"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/T11130","display_name":"Coding theory and cryptography","score":0.4749000072479248,"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":0.4749000072479248,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.21899999678134918,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.11500000208616257,"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/finite-field","display_name":"Finite field","score":0.5342000126838684},{"id":"https://openalex.org/keywords/galois-theory","display_name":"Galois theory","score":0.5127999782562256},{"id":"https://openalex.org/keywords/skew","display_name":"Skew","score":0.4903999865055084},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.475600004196167},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.45320001244544983},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4343999922275543},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.40450000762939453},{"id":"https://openalex.org/keywords/galois-group","display_name":"Galois group","score":0.4016000032424927},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.38679999113082886}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7839999794960022},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.5342000126838684},{"id":"https://openalex.org/C94398972","wikidata":"https://www.wikidata.org/wiki/Q92552","display_name":"Galois theory","level":2,"score":0.5127999782562256},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.4903999865055084},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.475600004196167},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46470001339912415},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.45320001244544983},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4343999922275543},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.40450000762939453},{"id":"https://openalex.org/C67536143","wikidata":"https://www.wikidata.org/wiki/Q730384","display_name":"Galois group","level":2,"score":0.4016000032424927},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.38679999113082886},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.38589999079704285},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.38119998574256897},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.37700000405311584},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3424000144004822},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3301999866962433},{"id":"https://openalex.org/C191421660","wikidata":"https://www.wikidata.org/wiki/Q829546","display_name":"Primality test","level":3,"score":0.3280999958515167},{"id":"https://openalex.org/C156350748","wikidata":"https://www.wikidata.org/wiki/Q5513324","display_name":"GF(2)","level":3,"score":0.3208000063896179},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3179999887943268},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.29010000824928284},{"id":"https://openalex.org/C35435516","wikidata":"https://www.wikidata.org/wiki/Q5370016","display_name":"Embedding problem","level":3,"score":0.28630000352859497},{"id":"https://openalex.org/C15927051","wikidata":"https://www.wikidata.org/wiki/Q246593","display_name":"Cryptographic primitive","level":4,"score":0.2759000062942505},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.26750001311302185},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C185592164","wikidata":"https://www.wikidata.org/wiki/Q1052579","display_name":"Unique factorization domain","level":3,"score":0.2644999921321869},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.25049999356269836}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2512.17256","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.17256","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2512.17256","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.17256","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"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":{"Let":[0],"$p$":[1],"be":[2,7],"a":[3],"prime":[4],"and":[5,21,44,75,122,152],"$s,m,n$":[6],"positive":[8],"integers.":[9],"This":[10,113],"paper":[11],"studies":[12],"quasi-recursive":[13,56,107],"MDS":[14,57,70,108],"matrices":[15,54,109],"over":[16,110,157],"Galois":[17,111],"rings":[18,37],"$GR(p^{s},":[19,38],"p^{sm})$":[20],"proposes":[22],"various":[23],"direct":[24],"construction":[25,31],"methods":[26,96],"for":[27,64,145],"such":[28],"matrices.":[29,58],"The":[30,140],"is":[32,80,163],"based":[33],"on":[34],"skew":[35,101],"polynomial":[36],"p^{sm})[X;\u03c3]$,":[39],"whose":[40],"rich":[41],"factorization":[42],"properties":[43],"enlarged":[45],"class":[46],"of":[47,84,88,127,164],"polynomials":[48,66,102],"are":[49,62,97,142],"used":[50],"to":[51,99,106,118,133],"define":[52],"companion":[53],"generating":[55],"First,":[59],"two":[60],"criteria":[61],"established":[63],"characterizing":[65],"that":[67,103],"yield":[68],"recursive":[69],"matrices,":[71,129],"generalizing":[72],"existing":[73],"results,":[74],"then":[76],"an":[77],"additional":[78],"criterion":[79],"derived":[81],"in":[82,137,167],"terms":[83],"the":[85,89,119,125,158],"right":[86],"roots":[87],"associated":[90],"Wedderburn":[91],"polynomial.":[92],"Using":[93],"these":[94],"criteria,":[95],"developed":[98],"construct":[100],"give":[104],"rise":[105],"rings.":[112],"framework":[114],"extends":[115],"known":[116],"constructions":[117],"non-commutative":[120],"setting":[121],"significantly":[123],"enlarges":[124],"family":[126],"available":[128],"with":[130],"potential":[131],"applications":[132],"efficient":[134],"diffusion":[135],"layers":[136],"cryptographic":[138,169],"primitives.":[139],"results":[141],"particularly":[143],"relevant":[144],"practical":[146],"implementations":[147],"when":[148],"$s":[149],"=":[150,154],"1$":[151],"$p":[153],"2$,":[155],"i.e.,":[156],"finite":[159],"field":[160],"$\\mathbb{F}_{2^m}$,":[161],"which":[162],"central":[165],"interest":[166],"real-world":[168],"applications.":[170]},"counts_by_year":[],"updated_date":"2025-12-23T23:15:37.779995","created_date":"2025-12-23T00:00:00"}
