{"id":"https://openalex.org/W7223945462","doi":"https://doi.org/10.5281/zenodo.23701586","title":"Two Sparse Binary Operators with Optimal Generating Length","display_name":"Two Sparse Binary Operators with Optimal Generating Length","publication_year":2026,"publication_date":"2026-10-27","ids":{"openalex":"https://openalex.org/W7223945462","doi":"https://doi.org/10.5281/zenodo.23701586"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23701586","doi":"https://doi.org/10.5281/zenodo.23701586","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23701586","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23701586","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159976007","display_name":"lmtlssss\ud83d\udf10","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"lmtlssss\ud83d\udf10","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5159976007"],"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.47189998626708984,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.47189998626708984,"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/T10849","display_name":"Finite Group Theory Research","score":0.22840000689029694,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.12460000067949295,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/matrix-algebra","display_name":"matrix algebra","score":0.527999997138977},{"id":"https://openalex.org/keywords/rank-one-matrices","display_name":"rank-one matrices","score":0.7039999961853027},{"id":"https://openalex.org/keywords/characteristic-2","display_name":"characteristic 2","score":0.6620000004768372},{"id":"https://openalex.org/keywords/invariant-subspaces","display_name":"invariant subspaces","score":0.7429999709129333},{"id":"https://openalex.org/keywords/linear-quotients","display_name":"linear quotients","score":0.9079999923706055},{"id":"https://openalex.org/keywords/binary-vector-spaces","display_name":"binary vector spaces","score":0.527999997138977}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8166000247001648},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.6575000286102295},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5667999982833862},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5414000153541565},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5001999735832214},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4966000020503998},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45320001244544983},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.424699991941452},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.3937999904155731},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.38670000433921814},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.38100001215934753},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.37470000982284546},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.37389999628067017},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.365200012922287},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.3617999851703644},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.358599990606308},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.3569999933242798},{"id":"https://openalex.org/C163561899","wikidata":"https://www.wikidata.org/wiki/Q1994977","display_name":"Logical matrix","level":3,"score":0.35589998960494995},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.353300005197525},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.35089999437332153},{"id":"https://openalex.org/C27563320","wikidata":"https://www.wikidata.org/wiki/Q650670","display_name":"Nilpotent matrix","level":5,"score":0.3382999897003174},{"id":"https://openalex.org/C185529760","wikidata":"https://www.wikidata.org/wiki/Q164307","display_name":"Binary operation","level":2,"score":0.3375000059604645},{"id":"https://openalex.org/C62555958","wikidata":"https://www.wikidata.org/wiki/Q6042601","display_name":"Integer matrix","level":5,"score":0.32710000872612},{"id":"https://openalex.org/C42321380","wikidata":"https://www.wikidata.org/wiki/Q849705","display_name":"Characteristic polynomial","level":3,"score":0.3246000111103058},{"id":"https://openalex.org/C134765980","wikidata":"https://www.wikidata.org/wiki/Q879126","display_name":"Bitwise operation","level":2,"score":0.31630000472068787},{"id":"https://openalex.org/C3019018024","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear operators","level":3,"score":0.31209999322891235},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.31060001254081726},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.30149999260902405},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.3003000020980835},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.2985999882221222},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.2897999882698059},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28929999470710754},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2892000079154968},{"id":"https://openalex.org/C141495983","wikidata":"https://www.wikidata.org/wiki/Q814361","display_name":"Companion matrix","level":5,"score":0.28600001335144043},{"id":"https://openalex.org/C96865113","wikidata":"https://www.wikidata.org/wiki/Q2946816","display_name":"Certificate","level":2,"score":0.26809999346733093},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.2619999945163727},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.25690001249313354}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23701586","doi":"https://doi.org/10.5281/zenodo.23701586","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23701586","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"Preprint"},{"id":"doi:10.5281/zenodo.23701587","doi":"https://doi.org/10.5281/zenodo.23701587","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23701587","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23701586","doi":"https://doi.org/10.5281/zenodo.23701586","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23701586","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2035859536","https://openalex.org/W3123084253","https://openalex.org/W2052070704","https://openalex.org/W7215282230","https://openalex.org/W4413389370","https://openalex.org/W7096731697","https://openalex.org/W2906303781","https://openalex.org/W2154909530","https://openalex.org/W7203672198","https://openalex.org/W1985788618"],"abstract_inverted_index":{"We":[0],"consider":[1],"two":[2,59],"specified":[3],"rotation-and-shift":[4],"operators":[5],"on":[6],"a":[7,68],"32-dimensional":[8],"binary":[9],"vector":[10],"space.":[11],"Their":[12],"unital":[13],"algebra":[14],"is":[15,24],"the":[16,27,89],"full":[17],"matrix":[18,36,57,66],"algebra,":[19],"and":[20,58,88,95],"their":[21],"generating":[22],"length":[23,45],"exactly":[25],"ten,":[26],"smallest":[28],"possible":[29],"value":[30],"for":[31,91],"any":[32],"pair":[33],"of":[34,44,78],"32-by-32":[35],"generators.":[37],"A":[38,49],"certificate":[39],"supplies":[40],"1,024":[41],"independent":[42,86],"words":[43],"at":[46],"most":[47],"ten.":[48],"second":[50],"proof":[51],"gives":[52],"an":[53],"explicit":[54],"polynomial":[55],"rank-one":[56],"cyclic":[60],"bases.":[61],"These":[62],"bases":[63],"construct":[64],"every":[65,76],"by":[67],"unique":[69],"coefficient":[70],"array.":[71],"The":[72,81],"conclusions":[73],"hold":[74],"over":[75],"field":[77],"characteristic":[79],"two.":[80],"paper":[82],"includes":[83],"exact":[84],"certificates,":[85],"verification,":[87],"consequences":[90],"simultaneous":[92],"invariant":[93],"subspaces":[94],"linear":[96],"quotients.":[97]},"counts_by_year":[],"updated_date":"2026-10-29T09:56:32.521200","created_date":"2026-10-28T00:00:00"}
