{"id":"https://openalex.org/W1656340913","doi":"https://doi.org/10.1109/isit.2015.7282449","title":"Binary nonlinear kernels of maximum exponents of polar codes of dimensions up to sixteen","display_name":"Binary nonlinear kernels of maximum exponents of polar codes of dimensions up to sixteen","publication_year":2015,"publication_date":"2015-06-01","ids":{"openalex":"https://openalex.org/W1656340913","doi":"https://doi.org/10.1109/isit.2015.7282449","mag":"1656340913"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2015.7282449","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2015.7282449","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"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/A5048471624","display_name":"Hsien-Ping Lin","orcid":"https://orcid.org/0000-0002-7244-3375"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Hsien-Ping Lin","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California, Davis, CA, USA","Dept. of Electrical and Computer Engineering, University of California, Davis 95616, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California, Davis, CA, USA","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"Dept. of Electrical and Computer Engineering, University of California, Davis 95616, USA","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100772114","display_name":"Shu Lin","orcid":"https://orcid.org/0000-0003-1401-7834"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shu Lin","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California, Davis, CA, USA","Dept. of Electrical and Computer Engineering, University of California, Davis 95616, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California, Davis, CA, USA","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"Dept. of Electrical and Computer Engineering, University of California, Davis 95616, USA","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102938606","display_name":"Khaled Abdel-Ghaffar","orcid":"https://orcid.org/0000-0002-3128-0557"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Khaled Abdel-Ghaffar","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California, Davis, CA, USA","Dept. of Electrical and Computer Engineering, University of California, Davis 95616, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California, Davis, CA, USA","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"Dept. of Electrical and Computer Engineering, University of California, Davis 95616, USA","institution_ids":["https://openalex.org/I84218800"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5048471624"],"corresponding_institution_ids":["https://openalex.org/I84218800"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.04789015,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":null,"issue":null,"first_page":"221","last_page":"225"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9991999864578247,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.8213979005813599},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.7147756218910217},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6927280426025391},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5315437316894531},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4716840386390686},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.4361611604690552},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4345608949661255},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3973942995071411},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37778186798095703},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19637957215309143},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12969836592674255},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12116178870201111},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.09268301725387573},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0896361768245697}],"concepts":[{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.8213979005813599},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7147756218910217},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6927280426025391},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5315437316894531},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4716840386390686},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.4361611604690552},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4345608949661255},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3973942995071411},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37778186798095703},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19637957215309143},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12969836592674255},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12116178870201111},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.09268301725387573},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0896361768245697},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2015.7282449","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2015.7282449","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320308204","display_name":"Northrop Grumman","ror":"https://ror.org/05kewds18"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W109405981","https://openalex.org/W1948635384","https://openalex.org/W1975096885","https://openalex.org/W1984960835","https://openalex.org/W2010238614","https://openalex.org/W2025204728","https://openalex.org/W2038681062","https://openalex.org/W2055534149","https://openalex.org/W2104558348","https://openalex.org/W2119461808","https://openalex.org/W2125761068","https://openalex.org/W2139784773","https://openalex.org/W2145712176","https://openalex.org/W2150498905","https://openalex.org/W6604469142","https://openalex.org/W6664206675","https://openalex.org/W6677689312"],"related_works":["https://openalex.org/W2089892314","https://openalex.org/W1603091392","https://openalex.org/W4386075310","https://openalex.org/W2095626363","https://openalex.org/W2169565408","https://openalex.org/W2127229869","https://openalex.org/W3123056048","https://openalex.org/W2150638158","https://openalex.org/W2121506664","https://openalex.org/W2363184354"],"abstract_inverted_index":{"Polar":[0],"codes":[1],"proposed":[2,91],"by":[3,48,92,102],"Arikan":[4],"are":[5,30,110,137],"based":[6],"on":[7],"a":[8,50,55,60,76,121],"linear":[9,52,89,122],"kernel":[10,53,58,77,90],"of":[11,22,25,36,87,118,120,126],"dimension":[12,37,71],"two":[13],"with":[14,59,78,107,113],"exponent":[15,42,79,86],"0.5.":[16],"In":[17],"this":[18],"paper,":[19],"binary":[20],"kernels":[21,112,125],"maximum":[23,41,131],"exponents":[24,114],"dimensions":[26,97,128],"up":[27],"to":[28,45],"16":[29],"presented":[31],"except":[32],"for":[33,72],"the":[34,40,69,85,88],"case":[35],"12":[38],"where":[39],"is":[43,94],"shown":[44],"be":[46],"attained":[47],"either":[49],"constructed":[51],"or":[54,143],"possible":[56],"nonlinear":[57,111,134],"specified":[61],"partial":[62],"distance":[63],"sequence.":[64],"The":[65,124],"results":[66],"show":[67],"that":[68,119,129],"minimum":[70],"which":[73],"there":[74,109],"exists":[75],"greater":[80],"than":[81,116],"0.5,":[82],"i.e.,":[83],"exceeds":[84],"Arikan,":[93],"14.":[95],"For":[96],"14,":[98],"15,":[99],"16,":[100],"discussed":[101],"Presman":[103],"et":[104],"al.,":[105],"along":[106],"13,":[108],"larger":[115],"any":[117],"kernel.":[123],"these":[127],"have":[130],"exponent,":[132],"although":[133],"over":[135],"GF(2),":[136],"\u2124":[138,144,148],"<sub":[139,145,149],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[140,146,150],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">4</sub>":[141,151],"-linear":[142],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[147],"-linear.":[152]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}