{"id":"https://openalex.org/W7223889682","doi":"https://doi.org/10.48550/arxiv.2610.33903","title":"On Reed-Muller-Type Codes Associated to Proto-Exact Categories","display_name":"On Reed-Muller-Type Codes Associated to Proto-Exact Categories","publication_year":2026,"publication_date":"2026-10-24","ids":{"openalex":"https://openalex.org/W7223889682","doi":"https://doi.org/10.48550/arxiv.2610.33903"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.33903","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33903","pdf_url":"https://arxiv.org/pdf/2610.33903","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.33903","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077283887","display_name":"Jeremy R. Edison","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I50702494","display_name":"Milwaukee School of Engineering","ror":"https://ror.org/04h7cfr36","country_code":"US","type":"education","lineage":["https://openalex.org/I50702494"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Edison, Jeremy","raw_affiliation_strings":["Department of Mathematics , Milwaukee School of Engineering , WI , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Milwaukee School of Engineering , WI , USA","institution_ids":["https://openalex.org/I50702494"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037140345","display_name":"Alexander Harris Sistko","orcid":"https://orcid.org/0000-0001-7576-8709","observed_orcids":["https://orcid.org/0000-0001-7576-8709"]},"institutions":[{"id":"https://openalex.org/I157455823","display_name":"SUNY New Paltz","ror":"https://ror.org/03j3dv688","country_code":"US","type":"education","lineage":["https://openalex.org/I157455823"]},{"id":"https://openalex.org/I50702494","display_name":"Milwaukee School of Engineering","ror":"https://ror.org/04h7cfr36","country_code":"US","type":"education","lineage":["https://openalex.org/I50702494"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sistko, Alexander","raw_affiliation_strings":["Department of Mathematics , Milwaukee School of Engineering , WI , USA","Department of Mathematics , State University of New York at New Paltz , NY , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Milwaukee School of Engineering , WI , USA","institution_ids":["https://openalex.org/I50702494"]},{"raw_affiliation_string":"Department of Mathematics , State University of New York at New Paltz , NY , USA","institution_ids":["https://openalex.org/I157455823"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.5268999934196472,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.5268999934196472,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11130","display_name":"Coding theory and cryptography","score":0.4004000127315521,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.03790000081062317,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/reed-muller-codes","display_name":"Reed-Muller codes","score":0.9879999756813049},{"id":"https://openalex.org/keywords/binary-linear-block-codes","display_name":"binary linear block codes","score":0.8159999847412109},{"id":"https://openalex.org/keywords/root-systems","display_name":"root systems","score":0.8009999990463257},{"id":"https://openalex.org/keywords/algebraic-geometry-codes","display_name":"algebraic geometry codes","score":0.972000002861023},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"minimum distance","score":0.7990000247955322}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7702000141143799},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5874999761581421},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5569000244140625},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5235000252723694},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4779999852180481},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46050000190734863},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4593999981880188},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43149998784065247},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.421999990940094},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4187000095844269},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37439998984336853},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.357699990272522},{"id":"https://openalex.org/C109593458","wikidata":"https://www.wikidata.org/wiki/Q5262626","display_name":"Derived category","level":3,"score":0.3467000126838684},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3409999907016754},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.3156000077724457},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.31349998712539673},{"id":"https://openalex.org/C2780617661","wikidata":"https://www.wikidata.org/wiki/Q541563","display_name":"Subcategory","level":2,"score":0.31349998712539673},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3028999865055084},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.29350000619888306},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.2930000126361847},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.290800005197525},{"id":"https://openalex.org/C65180967","wikidata":"https://www.wikidata.org/wiki/Q130901","display_name":"Binary relation","level":2,"score":0.2879999876022339},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C72727785","wikidata":"https://www.wikidata.org/wiki/Q2518298","display_name":"Category of sets","level":3,"score":0.2696000039577484},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C7879355","wikidata":"https://www.wikidata.org/wiki/Q5135329","display_name":"Closed category","level":3,"score":0.2632000148296356},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2590000033378601},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.25360000133514404},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2529999911785126},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.33903","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33903","pdf_url":"https://arxiv.org/pdf/2610.33903","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2610.33903","doi":"https://doi.org/10.48550/arxiv.2610.33903","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.33903","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.33903","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33903","pdf_url":"https://arxiv.org/pdf/2610.33903","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223889682.pdf","grobid_xml":"https://content.openalex.org/works/W7223889682.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W6948149291"],"related_works":["https://openalex.org/W2043941000","https://openalex.org/W4407814140","https://openalex.org/W1537917416","https://openalex.org/W1648201366","https://openalex.org/W22865703","https://openalex.org/W2110349902","https://openalex.org/W1511348214","https://openalex.org/W2103797071","https://openalex.org/W4307782542","https://openalex.org/W1537590015"],"abstract_inverted_index":{"In":[0,88],"this":[1,42,71],"paper,":[2],"we":[3,73,102],"show":[4,103],"how":[5,104],"to":[6,15,61,84,105,121],"associate":[7],"a":[8,75,96],"family":[9,30,35,44,108],"of":[10,18,36,48,55,58,65,70,80,98,100,112,129,138,140],"binary":[11,37],"linear":[12],"block":[13],"codes":[14],"the":[16,33,53,89,92,110,130],"class":[17],"admissibly":[19],"cofinitary":[20],"objects":[21],"in":[22,116],"any":[23,85],"proto-exact":[24,93],"category":[25,79,94,97],"with":[26],"rank":[27],"function.":[28],"This":[29],"naturally":[31],"generalizes":[32],"well-studied":[34],"Reed-Muller":[38],"codes,":[39,115],"and":[40,132],"recovers":[41],"classical":[43],"for":[45,135],"suitable":[46],"choices":[47],"category.":[49],"We":[50,125],"also":[51],"expand":[52],"list":[54],"known":[56],"examples":[57],"proto-abelian":[59,78],"categories":[60,64],"include":[62],"incidence":[63],"posets.":[66],"As":[67],"an":[68,119],"application":[69],"result,":[72],"construct":[74],"binormal,":[76],"combinatorial,":[77],"Kashiwara":[81],"crystals":[82],"associated":[83],"root":[86],"system.":[87],"case":[90],"that":[91],"is":[95],"$\\mathbb{F}_1$-representations":[99,139],"quivers,":[101],"reconstruct":[106],"our":[107],"via":[109],"language":[111],"algebraic":[113],"geometry":[114],"particular":[117],"motivating":[118],"extension":[120],"arbitrary":[122],"finite":[123],"fields.":[124],"provide":[126],"explicit":[127],"computations":[128],"dimension":[131],"minimum":[133],"distance":[134],"select":[136],"families":[137],"quivers.":[141]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-28T00:00:00"}
