{"id":"https://openalex.org/W7100375487","doi":null,"title":"\\tQuantum Error Correction Via Codes Over GF(4)","display_name":"\\tQuantum Error Correction Via Codes Over GF(4)","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W7100375487"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.252.2489","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.252.2489","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/quant-ph/9608006v5.pdf","raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"A. R. Calderbank","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. R. Calderbank","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"E. M. Rains","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"E. M. Rains","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020744800","display_name":"Peter W. Shor","orcid":"https://orcid.org/0000-0003-4626-5648","observed_orcids":["https://orcid.org/0000-0003-4626-5648"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. W. Shor","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"N. J. A. Sloane","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"N. J. A. Sloane","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.8198000192642212,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.8198000192642212,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.17599999904632568,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.0006000000284984708,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"quantum error correction","score":0.9900000095367432},{"id":"https://openalex.org/keywords/quantum-error-correcting-codes","display_name":"quantum error-correcting codes","score":0.8420000076293945},{"id":"https://openalex.org/keywords/additive-codes","display_name":"additive codes","score":0.7129999995231628},{"id":"https://openalex.org/keywords/gf-4","display_name":"GF(4)","score":0.8479999899864197},{"id":"https://openalex.org/keywords/self-orthogonal-codes","display_name":"self-orthogonal codes","score":0.9319999814033508},{"id":"https://openalex.org/keywords/code-bounds","display_name":"code bounds","score":0.7210000157356262},{"id":"https://openalex.org/keywords/qubits","display_name":"qubits","score":0.6779999732971191}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5564000010490417},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.5084999799728394},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5045999884605408},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.45489999651908875},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.4456000030040741},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.41190001368522644},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.41110000014305115},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.39500001072883606},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3702999949455261},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.3662000000476837},{"id":"https://openalex.org/C45235069","wikidata":"https://www.wikidata.org/wiki/Q278425","display_name":"Table (database)","level":2,"score":0.3547999858856201},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3433000147342682},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.32989999651908875},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.314300000667572},{"id":"https://openalex.org/C64948573","wikidata":"https://www.wikidata.org/wiki/Q625117","display_name":"BCJR algorithm","level":5,"score":0.31380000710487366},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.305400013923645},{"id":"https://openalex.org/C114504821","wikidata":"https://www.wikidata.org/wiki/Q2164281","display_name":"Turbo code","level":3,"score":0.30090001225471497},{"id":"https://openalex.org/C157899210","wikidata":"https://www.wikidata.org/wiki/Q1395022","display_name":"Convolutional code","level":3,"score":0.29319998621940613},{"id":"https://openalex.org/C65058987","wikidata":"https://www.wikidata.org/wiki/Q7826005","display_name":"Tornado code","level":5,"score":0.28940001130104065},{"id":"https://openalex.org/C128151799","wikidata":"https://www.wikidata.org/wiki/Q13563306","display_name":"Luby transform code","level":5,"score":0.2838999927043915},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.2662999927997589},{"id":"https://openalex.org/C46462455","wikidata":"https://www.wikidata.org/wiki/Q5395712","display_name":"Error floor","level":4,"score":0.26170000433921814},{"id":"https://openalex.org/C103093684","wikidata":"https://www.wikidata.org/wiki/Q7094069","display_name":"Online codes","level":5,"score":0.25429999828338623},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.2526000142097473}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.252.2489","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.252.2489","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/quant-ph/9608006v5.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4394666094","https://openalex.org/W3196379218","https://openalex.org/W3008150897","https://openalex.org/W2219849163","https://openalex.org/W2950374282","https://openalex.org/W2126438119","https://openalex.org/W2572379384","https://openalex.org/W3023649483","https://openalex.org/W2885214910","https://openalex.org/W2148225705"],"abstract_inverted_index":{"The":[0],"problem":[1,10],"of":[2,11,43,51],"finding":[3,12],"quantum-error-correcting":[4],"codes":[5,14,32,50],"is":[6],"transformed":[7],"into":[8],"the":[9,16],"additive":[13],"over":[15],"field":[17],"GF(4)":[18],"which":[19],"are":[20,36],"self-orthogonal":[21],"with":[22],"respect":[23],"to":[24,54],"a":[25,41],"certain":[26],"trace":[27],"inner":[28],"product.":[29],"Many":[30],"new":[31,34],"and":[33,45],"bounds":[35,47],"presented,":[37],"as":[38,40],"well":[39],"table":[42],"upper":[44],"lower":[46],"on":[48],"such":[49],"length":[52],"up":[53],"30":[55],"qubits.":[56]},"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-27T00:00:00"}