{"id":"https://openalex.org/W2015466022","doi":"https://doi.org/10.1109/isit.2013.6620386","title":"Spherically punctured Reed-Muller codes","display_name":"Spherically punctured Reed-Muller codes","publication_year":2013,"publication_date":"2013-07-01","ids":{"openalex":"https://openalex.org/W2015466022","doi":"https://doi.org/10.1109/isit.2013.6620386","mag":"2015466022"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2013.6620386","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2013.6620386","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE International Symposium on Information Theory","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/A5003453269","display_name":"Olga Kapralova","orcid":"https://orcid.org/0000-0001-9130-4875"},"institutions":[{"id":"https://openalex.org/I103635307","display_name":"University of California, Riverside","ror":"https://ror.org/03nawhv43","country_code":"US","type":"education","lineage":["https://openalex.org/I103635307"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Olga Kapralova","raw_affiliation_strings":["Department of Electrical Engineering, University of California, Riverside, USA","Dept. of Electr. Eng., Univ. of California at Riverside, Riverside, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of California, Riverside, USA","institution_ids":["https://openalex.org/I103635307"]},{"raw_affiliation_string":"Dept. of Electr. Eng., Univ. of California at Riverside, Riverside, CA, USA","institution_ids":["https://openalex.org/I103635307"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059701662","display_name":"Ilya Dumer","orcid":"https://orcid.org/0000-0002-0884-9389"},"institutions":[{"id":"https://openalex.org/I103635307","display_name":"University of California, Riverside","ror":"https://ror.org/03nawhv43","country_code":"US","type":"education","lineage":["https://openalex.org/I103635307"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ilya Dumer","raw_affiliation_strings":["Department of Electrical Engineering, University of California, Riverside, USA","Dept. of Electr. Eng., Univ. of California at Riverside, Riverside, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of California, Riverside, USA","institution_ids":["https://openalex.org/I103635307"]},{"raw_affiliation_string":"Dept. of Electr. Eng., Univ. of California at Riverside, Riverside, CA, USA","institution_ids":["https://openalex.org/I103635307"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I103635307"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.07903886,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1047","last_page":"1051"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9991000294685364,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9965000152587891,"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/hypercube","display_name":"Hypercube","score":0.7076371908187866},{"id":"https://openalex.org/keywords/tuple","display_name":"Tuple","score":0.6993103623390198},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.6674980521202087},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.6230286359786987},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5135176777839661},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.48174357414245605},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45888596773147583},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3772655129432678},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3600815534591675},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34114229679107666},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.16445747017860413},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.08879286050796509},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.0772123634815216}],"concepts":[{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.7076371908187866},{"id":"https://openalex.org/C118930307","wikidata":"https://www.wikidata.org/wiki/Q600590","display_name":"Tuple","level":2,"score":0.6993103623390198},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.6674980521202087},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.6230286359786987},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5135176777839661},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.48174357414245605},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45888596773147583},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3772655129432678},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3600815534591675},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34114229679107666},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.16445747017860413},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.08879286050796509},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0772123634815216},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2013.6620386","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2013.6620386","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337392","display_name":"Division of Electrical, Communications and Cyber Systems","ror":"https://ror.org/01krpsy48"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1606480398","https://openalex.org/W2014235620","https://openalex.org/W2054471150","https://openalex.org/W2065465262","https://openalex.org/W2103524940","https://openalex.org/W2132955525","https://openalex.org/W2150498905"],"related_works":["https://openalex.org/W2943247777","https://openalex.org/W2740543340","https://openalex.org/W2371167013","https://openalex.org/W1582340598","https://openalex.org/W1541021634","https://openalex.org/W2779867339","https://openalex.org/W2794545997","https://openalex.org/W2584980534","https://openalex.org/W2098310607","https://openalex.org/W2114720447"],"abstract_inverted_index":{"Consider":[0],"a":[1,37,45,72],"binary":[2],"Reed-Muller":[3,26],"code":[4,106],"RM(r,":[5],"m)":[6],"defined":[7],"on":[8],"the":[9,58,67,92],"m-dimensional":[10],"hypercube":[11],"F":[12],"<sup":[13],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[14,17,30,84],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">m</sup>":[15],"<sub":[16,29,83],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[18],".":[19],"In":[20],"this":[21],"paper,":[22],"we":[23],"study":[24],"punctured":[25,51],"codes":[27,52,61,81,102],"P":[28,82],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">r</sub>":[31,85],"(m,":[32,86],"b)":[33,87],"whose":[34],"positions":[35],"form":[36],"spherical":[38,73],"b-layer":[39,74],"and":[40,62,103,115],"include":[41],"all":[42],"m-tuples":[43],"of":[44,57,77,100,111],"given":[46],"Hamming":[47],"weight":[48],"b.":[49,116],"These":[50],"inherit":[53],"some":[54],"recursive":[55,93,98],"properties":[56,99],"original":[59],"RM":[60],"can":[63],"be":[64,89],"built":[65],"from":[66],"shorter":[68],"codes,":[69],"by":[70,91],"decomposing":[71],"into":[75],"sub-layers":[76],"smaller":[78],"dimensions.":[79],"However,":[80],"cannot":[88],"formed":[90],"Plotkin":[94],"construction.":[95],"We":[96],"analyze":[97],"these":[101],"find":[104],"their":[105],"distances":[107],"for":[108],"arbitrary":[109],"values":[110],"parameters":[112],"r,":[113],"m,":[114]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
