{"id":"https://openalex.org/W2127780167","doi":"https://doi.org/10.1162/neco_a_00459","title":"Combinatorial Neural Codes from a Mathematical Coding Theory Perspective","display_name":"Combinatorial Neural Codes from a Mathematical Coding Theory Perspective","publication_year":2013,"publication_date":"2013-05-31","ids":{"openalex":"https://openalex.org/W2127780167","doi":"https://doi.org/10.1162/neco_a_00459","mag":"2127780167","pmid":"https://pubmed.ncbi.nlm.nih.gov/23724797"},"language":"en","primary_location":{"id":"doi:10.1162/neco_a_00459","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_00459","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020021216","display_name":"Carina Curto","orcid":"https://orcid.org/0000-0001-9849-3592"},"institutions":[{"id":"https://openalex.org/I114395901","display_name":"University of Nebraska\u2013Lincoln","ror":"https://ror.org/043mer456","country_code":"US","type":"education","lineage":["https://openalex.org/I114395901"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Carina Curto","raw_affiliation_strings":["Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, U.S.A","institution_ids":["https://openalex.org/I114395901"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050098453","display_name":"Vladimir Itskov","orcid":"https://orcid.org/0000-0002-7619-7255"},"institutions":[{"id":"https://openalex.org/I114395901","display_name":"University of Nebraska\u2013Lincoln","ror":"https://ror.org/043mer456","country_code":"US","type":"education","lineage":["https://openalex.org/I114395901"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vladimir Itskov","raw_affiliation_strings":["Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, U.S.A","institution_ids":["https://openalex.org/I114395901"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073186807","display_name":"Katherine Morrison","orcid":"https://orcid.org/0000-0002-8402-3212"},"institutions":[{"id":"https://openalex.org/I114395901","display_name":"University of Nebraska\u2013Lincoln","ror":"https://ror.org/043mer456","country_code":"US","type":"education","lineage":["https://openalex.org/I114395901"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Katherine Morrison","raw_affiliation_strings":["Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, U.S.A","institution_ids":["https://openalex.org/I114395901"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064782634","display_name":"Zachary Roth","orcid":null},"institutions":[{"id":"https://openalex.org/I114395901","display_name":"University of Nebraska\u2013Lincoln","ror":"https://ror.org/043mer456","country_code":"US","type":"education","lineage":["https://openalex.org/I114395901"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zachary Roth","raw_affiliation_strings":["Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, U.S.A","institution_ids":["https://openalex.org/I114395901"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024157334","display_name":"Judy L. Walker","orcid":null},"institutions":[{"id":"https://openalex.org/I114395901","display_name":"University of Nebraska\u2013Lincoln","ror":"https://ror.org/043mer456","country_code":"US","type":"education","lineage":["https://openalex.org/I114395901"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Judy L. Walker","raw_affiliation_strings":["Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, U.S.A","institution_ids":["https://openalex.org/I114395901"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I114395901"],"apc_list":null,"apc_paid":null,"fwci":1.8462,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.84976132,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"25","issue":"7","first_page":"1891","last_page":"1925"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10448","display_name":"Memory and Neural Mechanisms","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9894000291824341,"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/coding-theory","display_name":"Coding theory","score":0.7650305032730103},{"id":"https://openalex.org/keywords/receptive-field","display_name":"Receptive field","score":0.6567913293838501},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.6400856971740723},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.614517331123352},{"id":"https://openalex.org/keywords/neural-coding","display_name":"Neural coding","score":0.597172737121582},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5700677037239075},{"id":"https://openalex.org/keywords/redundancy","display_name":"Redundancy (engineering)","score":0.5501703023910522},{"id":"https://openalex.org/keywords/error-detection-and-correction","display_name":"Error detection and correction","score":0.470878928899765},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.466856986284256},{"id":"https://openalex.org/keywords/mathematical-theory","display_name":"Mathematical theory","score":0.4581301808357239},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45259758830070496},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.4352731704711914},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3348434567451477},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3171736001968384},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08415824174880981}],"concepts":[{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.7650305032730103},{"id":"https://openalex.org/C19071747","wikidata":"https://www.wikidata.org/wiki/Q1755207","display_name":"Receptive field","level":2,"score":0.6567913293838501},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.6400856971740723},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.614517331123352},{"id":"https://openalex.org/C77637269","wikidata":"https://www.wikidata.org/wiki/Q7002051","display_name":"Neural coding","level":2,"score":0.597172737121582},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5700677037239075},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.5501703023910522},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.470878928899765},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.466856986284256},{"id":"https://openalex.org/C2779193601","wikidata":"https://www.wikidata.org/wiki/Q20026918","display_name":"Mathematical theory","level":2,"score":0.4581301808357239},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45259758830070496},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.4352731704711914},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3348434567451477},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3171736001968384},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08415824174880981},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D007257","descriptor_name":"Information Theory","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D007257","descriptor_name":"Information Theory","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D007257","descriptor_name":"Information Theory","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008433","descriptor_name":"Mathematics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008433","descriptor_name":"Mathematics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008433","descriptor_name":"Mathematics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D009415","descriptor_name":"Nerve Net","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009415","descriptor_name":"Nerve Net","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009415","descriptor_name":"Nerve Net","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false}],"locations_count":3,"locations":[{"id":"doi:10.1162/neco_a_00459","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_00459","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:23724797","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/23724797","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural computation","raw_type":null},{"id":"pmh:oai:digitalcommons.unl.edu:mathfacpub-1061","is_oa":false,"landing_page_url":"https://digitalcommons.unl.edu/mathfacpub/62","pdf_url":null,"source":{"id":"https://openalex.org/S4306513441","display_name":"Insecta mundi","issn_l":"0749-6737","issn":["0749-6737","1942-1354","1942-1362"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310316217","host_organization_name":"Center for Systematic Entomology","host_organization_lineage":["https://openalex.org/P4310316217"],"host_organization_lineage_names":["Center for Systematic Entomology"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications, Department of Mathematics","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W81409850","https://openalex.org/W1496108277","https://openalex.org/W1536990343","https://openalex.org/W1557376630","https://openalex.org/W1559343931","https://openalex.org/W1572294349","https://openalex.org/W1593079125","https://openalex.org/W1606480398","https://openalex.org/W1619416921","https://openalex.org/W1867287134","https://openalex.org/W1908414974","https://openalex.org/W1978497623","https://openalex.org/W1981315681","https://openalex.org/W1984931175","https://openalex.org/W1986329333","https://openalex.org/W1993197592","https://openalex.org/W1995875735","https://openalex.org/W1998050452","https://openalex.org/W2004281974","https://openalex.org/W2008240154","https://openalex.org/W2008936540","https://openalex.org/W2016302674","https://openalex.org/W2023097449","https://openalex.org/W2045593108","https://openalex.org/W2052362533","https://openalex.org/W2052515926","https://openalex.org/W2065465262","https://openalex.org/W2077554996","https://openalex.org/W2083250197","https://openalex.org/W2096110699","https://openalex.org/W2097560155","https://openalex.org/W2099111195","https://openalex.org/W2100259206","https://openalex.org/W2101101880","https://openalex.org/W2102866130","https://openalex.org/W2109387052","https://openalex.org/W2115348689","https://openalex.org/W2116811583","https://openalex.org/W2120819568","https://openalex.org/W2122741244","https://openalex.org/W2124338387","https://openalex.org/W2130055919","https://openalex.org/W2133877521","https://openalex.org/W2147103442","https://openalex.org/W2147238273","https://openalex.org/W2150240029","https://openalex.org/W2152435897","https://openalex.org/W2152587044","https://openalex.org/W2155494892","https://openalex.org/W2157154487","https://openalex.org/W2170369633","https://openalex.org/W2478708596","https://openalex.org/W2993383518","https://openalex.org/W3022219149","https://openalex.org/W4206184909","https://openalex.org/W4206775542","https://openalex.org/W4234824781"],"related_works":["https://openalex.org/W2001657514","https://openalex.org/W2058670155","https://openalex.org/W2567723663","https://openalex.org/W2536752040","https://openalex.org/W2145889472","https://openalex.org/W2014480538","https://openalex.org/W3131160729","https://openalex.org/W1593079125","https://openalex.org/W2012355208","https://openalex.org/W2603429253"],"abstract_inverted_index":{"Shannon's":[0],"seminal":[1],"1948":[2],"work":[3],"gave":[4],"rise":[5],"to":[6,97,107,143],"two":[7],"distinct":[8],"areas":[9],"of":[10,60,75,91,99],"research:":[11],"information":[12,19],"theory":[13,20,33,53],"and":[14],"mathematical":[15,31,51],"coding":[16,32,52],"theory.":[17],"While":[18],"has":[21],"had":[22],"a":[23,42,50,104,133,140,146],"strong":[24],"influence":[25],"on":[26],"theoretical":[27],"neuroscience,":[28],"ideas":[29],"from":[30,49],"have":[34],"received":[35],"considerably":[36],"less":[37],"attention.":[38],"Here":[39],"we":[40],"take":[41],"new":[43],"look":[44],"at":[45,117],"combinatorial":[46],"neural":[47,147],"codes":[48,64,80,94,102,114,127],"perspective,":[54],"examining":[55],"the":[56,72,88,124],"error":[57,85,108,154],"correction":[58],"capabilities":[59],"familiar":[61],"receptive":[62,92,112],"field":[63,93,113],"(RF":[65],"codes).":[66],"We":[67,130],"find,":[68],"perhaps":[69],"surprisingly,":[70],"that":[71,98,132],"high":[73],"levels":[74],"redundancy":[76],"present":[77],"in":[78,135],"these":[79],"do":[81],"not":[82,152],"support":[83],"accurate":[84],"correction,":[86,155],"although":[87],"error-correcting":[89,136],"performance":[90],"catches":[95],"up":[96],"random":[100,125],"comparison":[101,126],"when":[103],"small":[105],"tolerance":[106],"is":[109],"introduced.":[110],"However,":[111],"are":[115,128],"good":[116],"reflecting":[118],"distances":[119],"between":[120,161],"represented":[121],"stimuli,":[122],"while":[123],"not.":[129],"suggest":[131],"compromise":[134],"capability":[137],"may":[138],"be":[139],"necessary":[141],"price":[142],"pay":[144],"for":[145],"code":[148],"whose":[149],"structure":[150],"serves":[151],"only":[153],"but":[156],"must":[157],"also":[158],"reflect":[159],"relationships":[160],"stimuli.":[162]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}