{"id":"https://openalex.org/W2010458273","doi":"https://doi.org/10.1109/arith.1987.6158714","title":"Error detection and correction for addition and subtraction, through use of higher radix extensions of hamming codes","display_name":"Error detection and correction for addition and subtraction, through use of higher radix extensions of hamming codes","publication_year":1987,"publication_date":"1987-05-01","ids":{"openalex":"https://openalex.org/W2010458273","doi":"https://doi.org/10.1109/arith.1987.6158714","mag":"2010458273"},"language":"en","primary_location":{"id":"doi:10.1109/arith.1987.6158714","is_oa":false,"landing_page_url":"https://doi.org/10.1109/arith.1987.6158714","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1987 IEEE 8th Symposium on Computer Arithmetic (ARITH)","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/A5112666383","display_name":"James E. Robertson","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"James E. Robertson","raw_affiliation_strings":["Department of Computer Science, University of Illinois, Urbana-Champaign, Urbana, IL, USA","Department of Computer Science, University of Illinois at Urbana-Champaign, 61801, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Illinois, Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Department of Computer Science, University of Illinois at Urbana-Champaign, 61801, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5112666383"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12026789,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"226","last_page":"229"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11005","display_name":"Radiation Effects in Electronics","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11005","display_name":"Radiation Effects in Electronics","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11032","display_name":"VLSI and Analog Circuit Testing","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.988099992275238,"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/modulo","display_name":"Modulo","score":0.8252145051956177},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.8060492277145386},{"id":"https://openalex.org/keywords/hamming","display_name":"Hamming(7,4)","score":0.7278069257736206},{"id":"https://openalex.org/keywords/error-detection-and-correction","display_name":"Error detection and correction","score":0.6803737878799438},{"id":"https://openalex.org/keywords/hamming-weight","display_name":"Hamming weight","score":0.6583849191665649},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.6301536560058594},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.6262833476066589},{"id":"https://openalex.org/keywords/subtraction","display_name":"Subtraction","score":0.5805092453956604},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.538487434387207},{"id":"https://openalex.org/keywords/cyclic-code","display_name":"Cyclic code","score":0.5120913982391357},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5094333291053772},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.45219549536705017},{"id":"https://openalex.org/keywords/carry","display_name":"Carry (investment)","score":0.43197330832481384},{"id":"https://openalex.org/keywords/adder","display_name":"Adder","score":0.4276476502418518},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3912060558795929},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39055687189102173},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.30632516741752625},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2563948631286621},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.17471808195114136},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.08928227424621582}],"concepts":[{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.8252145051956177},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.8060492277145386},{"id":"https://openalex.org/C112932734","wikidata":"https://www.wikidata.org/wiki/Q2322550","display_name":"Hamming(7,4)","level":5,"score":0.7278069257736206},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.6803737878799438},{"id":"https://openalex.org/C63361517","wikidata":"https://www.wikidata.org/wiki/Q5645805","display_name":"Hamming weight","level":5,"score":0.6583849191665649},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.6301536560058594},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.6262833476066589},{"id":"https://openalex.org/C68060419","wikidata":"https://www.wikidata.org/wiki/Q40754","display_name":"Subtraction","level":2,"score":0.5805092453956604},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.538487434387207},{"id":"https://openalex.org/C2096984","wikidata":"https://www.wikidata.org/wiki/Q245464","display_name":"Cyclic code","level":5,"score":0.5120913982391357},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5094333291053772},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.45219549536705017},{"id":"https://openalex.org/C2776299755","wikidata":"https://www.wikidata.org/wiki/Q432449","display_name":"Carry (investment)","level":2,"score":0.43197330832481384},{"id":"https://openalex.org/C164620267","wikidata":"https://www.wikidata.org/wiki/Q376953","display_name":"Adder","level":3,"score":0.4276476502418518},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3912060558795929},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39055687189102173},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.30632516741752625},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2563948631286621},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.17471808195114136},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.08928227424621582},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C82876162","wikidata":"https://www.wikidata.org/wiki/Q17096504","display_name":"Latency (audio)","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/arith.1987.6158714","is_oa":false,"landing_page_url":"https://doi.org/10.1109/arith.1987.6158714","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1987 IEEE 8th Symposium on Computer Arithmetic (ARITH)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2008960744","https://openalex.org/W2105471374","https://openalex.org/W1987803429","https://openalex.org/W2963549154","https://openalex.org/W2158117886","https://openalex.org/W1519122282","https://openalex.org/W1582340598","https://openalex.org/W2182731056","https://openalex.org/W2022910297","https://openalex.org/W2740543340"],"abstract_inverted_index":{"The":[0],"properties":[1],"of":[2,49,60],"Hamming":[3,50],"codes":[4,51],"for":[5,56],"error":[6],"detection":[7,57],"and":[8,32,36,58,65],"correction":[9,59],"can":[10,29],"be":[11,30],"extended":[12],"from":[13],"the":[14],"binary":[15],"parity":[16],"check":[17],"to":[18],"addition,":[19,26,38,44],"modulo":[20,27,45],"2r.":[21],"Malfunctions":[22],"in":[23,43],"hardware":[24,61],"during":[25,63],"2r,":[28,46],"detected":[31],"corrected.":[33],"Since":[34],"carry-save":[35,66],"signed-digit":[37,64],"radix":[39],"r,":[40],"are":[41],"included":[42],"this":[47],"extension":[48],"makes":[52],"possible":[53],"new":[54],"techniques":[55],"malfunctions":[62],"addition.":[67]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}