{"id":"https://openalex.org/W1484136811","doi":"https://doi.org/10.37236/2326","title":"On Codes that are Invariant under the Affine Group","display_name":"On Codes that are Invariant under the Affine Group","publication_year":2012,"publication_date":"2012-11-08","ids":{"openalex":"https://openalex.org/W1484136811","doi":"https://doi.org/10.37236/2326","mag":"1484136811"},"language":"en","primary_location":{"id":"doi:10.37236/2326","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2326","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i4p20/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i4p20/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015665731","display_name":"Peter Sin","orcid":"https://orcid.org/0000-0003-4493-7631"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Peter Sin","raw_affiliation_strings":["University of Florida","[University of Florida]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Florida","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"[University of Florida]","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015665731"],"corresponding_institution_ids":["https://openalex.org/I33213144"],"apc_list":null,"apc_paid":null,"fwci":0.4349,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.69986059,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"19","issue":"4","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":0.9994000196456909,"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":0.9994000196456909,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9929999709129333,"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"}},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.957099974155426,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8798220157623291},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.8267509937286377},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6805977821350098},{"id":"https://openalex.org/keywords/affine-space","display_name":"Affine space","score":0.6063534617424011},{"id":"https://openalex.org/keywords/algebraically-closed-field","display_name":"Algebraically closed field","score":0.5874839425086975},{"id":"https://openalex.org/keywords/affine-group","display_name":"Affine group","score":0.5850893259048462},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5842931866645813},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5143214464187622},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.49701669812202454},{"id":"https://openalex.org/keywords/general-linear-group","display_name":"General linear group","score":0.4121851325035095},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4113939702510834},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4046698808670044},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3917274475097656},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.1780516505241394}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8798220157623291},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.8267509937286377},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6805977821350098},{"id":"https://openalex.org/C173110770","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine space","level":3,"score":0.6063534617424011},{"id":"https://openalex.org/C203701370","wikidata":"https://www.wikidata.org/wiki/Q1047547","display_name":"Algebraically closed field","level":2,"score":0.5874839425086975},{"id":"https://openalex.org/C62623296","wikidata":"https://www.wikidata.org/wiki/Q686291","display_name":"Affine group","level":3,"score":0.5850893259048462},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5842931866645813},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5143214464187622},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.49701669812202454},{"id":"https://openalex.org/C172331165","wikidata":"https://www.wikidata.org/wiki/Q524607","display_name":"General linear group","level":3,"score":0.4121851325035095},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4113939702510834},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4046698808670044},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3917274475097656},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.1780516505241394},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","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},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/2326","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2326","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i4p20/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/2326","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2326","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i4p20/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1484136811.pdf","grobid_xml":"https://content.openalex.org/works/W1484136811.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1983430323","https://openalex.org/W1988239817","https://openalex.org/W2029905326","https://openalex.org/W2067213974","https://openalex.org/W2073236804","https://openalex.org/W2155052927","https://openalex.org/W2573792181","https://openalex.org/W4248513966"],"related_works":["https://openalex.org/W4385970665","https://openalex.org/W3022853753","https://openalex.org/W2953488600","https://openalex.org/W2951009501","https://openalex.org/W2052402162","https://openalex.org/W2914292729","https://openalex.org/W2045490549","https://openalex.org/W4386755331","https://openalex.org/W1974770915","https://openalex.org/W2388130124"],"abstract_inverted_index":{"Let":[0],"$k[V]$":[1,29],"be":[2],"the":[3,13,24,34,47,59],"space":[4,11],"of":[5,16,19,26,28,53],"functions":[6,54],"from":[7],"a":[8,42],"finite":[9],"vector":[10],"into":[12],"algebraically":[14],"closure":[15],"its":[17],"field":[18],"scalars.":[20],"This":[21],"paper":[22],"describes":[23],"lattice":[25],"subspaces":[27],"which":[30],"are":[31],"invariant":[32],"under":[33],"affine":[35],"group":[36],"${\\mathrm":[37],"AGL}(V)$.":[38],"The":[39],"description":[40],"provides":[41],"simple":[43],"method":[44],"for":[45],"finding":[46],"submodule":[48],"generated":[49],"by":[50],"any":[51],"set":[52],"given":[55],"as":[56],"polynomials":[57],"in":[58],"standard":[60],"coordinates.":[61]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
