[{"_1":2,"_3":-5,"_4":-5},"loaderData",{"_5":6,"_7":8,"_9":10},"actionData","errors","root",{"_262":263},"routes/_layout",{"_11":182},"routes/entity.$type.$id",{"_11":12,"_13":14,"_15":16,"_17":18,"_19":20,"_21":22,"_23":24,"_25":26,"_27":28},"dehydratedState",{"_73":74,"_75":76},"type","paper","id","paper_W2095418648","section","technologies","entity",{"_15":16,"_29":30,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":38,"_39":-5,"_40":41,"_42":43,"_44":45,"_46":47,"_48":-5,"_49":50,"_51":30,"_52":53,"_54":55,"_56":57,"_58":59,"_60":61,"_62":-5,"_63":64,"_65":-5,"_66":67,"_68":30,"_69":-5},"canonical","https://www.hugmap.com/entity/paper/paper_W2095418648/technologies","siteBaseUrl","https://www.hugmap.com","sectionCount",1,"jsonLd","{\"@context\":\"https://schema.org\",\"@graph\":[{\"name\":\"Error-Correcting Codes in Projective Space\",\"url\":\"https://www.hugmap.com/entity/paper/paper_W2095418648/technologies\",\"@type\":\"ScholarlyArticle\",\"headline\":\"Error-Correcting Codes in Projective Space\",\"datePublished\":\"2011-01-21\",\"isPartOf\":{\"@type\":\"Periodical\",\"name\":\"IEEE Transactions on Information Theory\"}},{\"@type\":\"CollectionPage\",\"name\":\"Error-Correcting Codes in Projective Space 相关技术\",\"description\":\"Error-Correcting Codes in Projective Space 在 HugMap 中的相关技术，共 1 条，含结构化关联信息与详情链接。\",\"url\":\"https://www.hugmap.com/entity/paper/paper_W2095418648/technologies\",\"inLanguage\":\"zh-CN\"},{\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"首页\",\"item\":\"https://www.hugmap.com/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"论文\",\"item\":\"https://www.hugmap.com/search?type=paper\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Error-Correcting Codes in Projective Space\",\"item\":\"https://www.hugmap.com/entity/paper/paper_W2095418648\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"相关技术\",\"item\":\"https://www.hugmap.com/entity/paper/paper_W2095418648/technologies\"}]}]}","name","Error-Correcting Codes in Projective Space","nameZh","aliases","description","descriptionZh","status","active","externalIds","{\"openalex\":\"W2095418648\",\"doi\":\"10.1109/tit.2010.2095232\"}","properties","source","openalex","createdAt","2026-05-21T16:11:01.197044389","updatedAt","2026-05-21T16:18:42.196150152","doi","10.1109/tit.2010.2095232","arxivId","openalexId","W2095418648","title","abstractText","The projective space of order n over the finite field \\BBF q , denoted here as Pq ( n ), is the set of all subspaces of the vector space \\BBF qn . The projective space can be endowed with the distance function d ( U , V ) = dim U + dim V -2 dim( U ∩ V ) which turns Pq ( n ) into a metric space. With this, an ( n , M , d ) code \\BBC in projective space is a subset of Pq ( n ) of size M such that the distance between any two codewords (subspaces) is at least d . Koetter and Kschischang recently showed that codes in projective space are precisely what is needed for error-correction in networks: an ( n , M , d ) code can correct t packet errors and ρ packet erasures introduced (adversarially) anywhere in the network as long as 2 t + 2ρ <; d . This motivates our interest in such codes. In this paper, we investigate certain basic aspects of “coding theory in projective space.” First, we present several new bounds on the size of codes in Pq ( n ), which may be thought of as counterparts of the classical bounds in coding theory due to Johnson, Delsarte, and Gilbert-Varshamov. Some of these are stronger than all the previously known bounds, at least for certain code parameters. We also present several specific constructions of codes and code families in Pq ( n ). Finally, we prove that nontrivial perfect codes in Pq ( n ) do not exist.","publishedDate","2011-01-21","publishedYear",2011,"venue","IEEE Transactions on Information Theory","citationCount",283,"authors","keywords",[70,71,72],"pdfUrl","topVenue",false,"displayName","displayDescription","Coding theory and cryptography","Cooperative Communication and Network Coding","Error Correcting Code Techniques","mutations",[],"queries",[77],{"_78":79,"_80":81,"_82":83,"_84":85},"dehydratedAt",1781591309107,"state",{"_87":88,"_89":26,"_90":79,"_91":-5,"_92":93,"_94":93,"_95":93,"_96":-5,"_97":-5,"_98":67,"_35":99,"_100":101},"queryKey",[86,19,14,16],"queryHash","[\"portal\",\"entity\",\"paper\",\"paper_W2095418648\"]","portal","data",{"_19":20,"_102":103,"_104":105,"_106":107,"_108":109,"_18":110,"_62":111},"dataUpdateCount","dataUpdatedAt","error","errorUpdateCount",0,"errorUpdatedAt","fetchFailureCount","fetchFailureReason","fetchMeta","isInvalidated","success","fetchStatus","idle","entityType","Paper","taxonomies",[150,151,152],"events",[],"articles",[],[135],[112,113],{"_15":129,"_29":130,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":131,"_39":-5,"_40":41,"_42":132,"_44":133,"_119":134,"_51":-5,"_121":-5,"_122":-5,"_123":-5,"_60":-5,"_124":-5,"_125":-5,"_126":-5,"_127":-5,"_128":-5,"_68":130,"_69":-5},{"_15":114,"_29":115,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":116,"_39":-5,"_40":41,"_42":117,"_44":118,"_119":120,"_51":-5,"_121":-5,"_122":-5,"_123":-5,"_60":-5,"_124":-5,"_125":-5,"_126":-5,"_127":-5,"_128":-5,"_68":115,"_69":-5},"person_A5062149532","Tuvi Etzion","{\"openalex\":\"A5062149532\",\"orcid\":\"0000-0002-4315-4400\"}","2026-05-21T16:11:01.465158654","2026-05-22T20:22:06.195585285","orcid","0000-0002-4315-4400","affiliation","researchArea","paperCount","homepage","linkedin","twitter","github","hindex","person_A5004102644","Alexander Vardy","{\"openalex\":\"A5004102644\",\"orcid\":\"0000-0003-3303-9078\"}","2026-05-14T05:26:59.244185363","2026-05-22T13:05:02.25940737","0000-0003-3303-9078",{"_15":136,"_29":71,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":137,"_39":-5,"_40":138,"_42":139,"_44":140,"_141":142,"_143":144,"_145":-5,"_146":147,"_148":-5,"_123":-5,"_149":-5,"_68":71,"_69":-5},"tech_oa_T10796","{\"taxonomy_id\":\"tax_rd_T10796\"}","openalex_topics","2026-05-17T09:00:35.178925188","2026-05-17T09:00:35.178928108","techType","architecture","domain","Physical Sciences","proposedYear","maturityLevel","growing","wikipediaUrl","patentCount",{"_15":176,"_29":70,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":177,"_39":-5,"_40":41,"_42":178,"_44":179,"_157":158,"_159":-5,"_160":161,"_162":180,"_164":181,"_166":93,"_167":168,"_169":93,"_170":-5,"_68":70,"_69":-5},{"_15":171,"_29":72,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":172,"_39":-5,"_40":41,"_42":173,"_44":174,"_157":158,"_159":-5,"_160":161,"_162":163,"_164":175,"_166":93,"_167":168,"_169":93,"_170":-5,"_68":72,"_69":-5},{"_15":153,"_29":71,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":154,"_39":-5,"_40":41,"_42":155,"_44":156,"_157":158,"_159":-5,"_160":161,"_162":163,"_164":165,"_166":93,"_167":168,"_169":93,"_170":-5,"_68":71,"_69":-5},"tax_rd_T10796","{\"openalex_topic\":\"T10796\"}","2026-05-14T01:01:36.418778051","2026-05-23T10:16:48.239268439","taxonomyType","RESEARCH_DOMAIN","code","level",3,"parentId","tax_rd_1705","path","Physical Sciences/Computer Science/Computer Networks and Communications/Cooperative Communication and Network Coding","sortOrder","isLeaf",true,"entityCount","children","tax_rd_T11321","{\"openalex_topic\":\"T11321\"}","2026-05-14T00:38:28.643553521","2026-05-23T11:05:42.212351184","Physical Sciences/Computer Science/Computer Networks and Communications/Error Correcting Code Techniques","tax_rd_T11130","{\"openalex_topic\":\"T11130\"}","2026-05-14T00:38:28.617637813","2026-05-23T12:17:43.257915081","tax_rd_1702","Physical Sciences/Computer Science/Artificial Intelligence/Coding theory and cryptography",{"_73":183,"_75":184},[],[185],{"_78":186,"_80":187,"_82":188,"_84":189},1781591304659,{"_87":191,"_89":26,"_90":186,"_91":-5,"_92":93,"_94":93,"_95":93,"_96":-5,"_97":-5,"_98":67,"_35":99,"_100":101},[86,190],"[\"portal\",\"industries\"]","industries",[192,193,194,195,196,197,198,199,200,201,202,203],{"_15":255,"_29":256,"_31":-5,"_32":257,"_33":258,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":207,"_42":-5,"_44":-5,"_157":208,"_159":-5,"_160":26,"_162":209,"_164":259,"_166":93,"_167":67,"_169":93,"_170":-5,"_68":256,"_69":258},{"_15":251,"_29":252,"_31":-5,"_32":-5,"_33":253,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":207,"_42":-5,"_44":-5,"_157":208,"_159":-5,"_160":26,"_162":209,"_164":254,"_166":93,"_167":67,"_169":93,"_170":-5,"_68":252,"_69":253},{"_15":245,"_29":246,"_31":-5,"_32":247,"_33":248,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":207,"_42":-5,"_44":-5,"_157":208,"_159":-5,"_160":26,"_162":209,"_164":249,"_166":93,"_167":67,"_169":93,"_170":-5,"_68":246,"_69":248},{"_15":241,"_29":242,"_31":-5,"_32":-5,"_33":243,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":207,"_42":-5,"_44":-5,"_157":208,"_159":-5,"_160":26,"_162":209,"_164":244,"_166":93,"_167":67,"_169":93,"_170":-5,"_68":242,"_69":243},{"_15":237,"_29":238,"_31":-5,"_32":-5,"_33":239,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":207,"_42":-5,"_44":-5,"_157":208,"_159":-5,"_160":26,"_162":209,"_164":240,"_166":93,"_167":67,"_169":93,"_170":-5,"_68":238,"_69":239},{"_15":231,"_29":232,"_31":-5,"_32":233,"_33":234,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":207,"_42":-5,"_44":-5,"_157":208,"_159":-5,"_160":26,"_162":209,"_164":235,"_166":93,"_167":67,"_169":93,"_170":-5,"_68":232,"_69":234},{"_15":227,"_29":228,"_31":-5,"_32":-5,"_33":229,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":207,"_42":-5,"_44":-5,"_157":208,"_159":-5,"_160":26,"_162":209,"_164":230,"_166":93,"_167":168,"_169":93,"_170":-5,"_68":228,"_69":229},{"_15":223,"_29":224,"_31":-5,"_32":-5,"_33":225,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":207,"_42":-5,"_44":-5,"_157":208,"_159":-5,"_160":26,"_162":209,"_164":226,"_166":93,"_167":67,"_169":93,"_170":-5,"_68":224,"_69":225},{"_15":219,"_29":220,"_31":-5,"_32":-5,"_33":221,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":207,"_42":-5,"_44":-5,"_157":208,"_159":-5,"_160":26,"_162":209,"_164":222,"_166":93,"_167":67,"_169":93,"_170":-5,"_68":220,"_69":221},{"_15":215,"_29":216,"_31":-5,"_32":-5,"_33":217,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":207,"_42":-5,"_44":-5,"_157":208,"_159":-5,"_160":26,"_162":209,"_164":218,"_166":93,"_167":67,"_169":93,"_170":-5,"_68":216,"_69":217},{"_15":211,"_29":212,"_31":-5,"_32":-5,"_33":213,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":207,"_42":-5,"_44":-5,"_157":208,"_159":-5,"_160":26,"_162":209,"_164":214,"_166":93,"_167":67,"_169":93,"_170":-5,"_68":212,"_69":213},{"_15":204,"_29":205,"_31":-5,"_32":-5,"_33":206,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":207,"_42":-5,"_44":-5,"_157":208,"_159":-5,"_160":26,"_162":209,"_164":210,"_166":93,"_167":67,"_169":93,"_170":-5,"_68":205,"_69":206},"tax_ind_smartphone","智能手机","Smartphone","manual","INDUSTRY","tax_ind_root","科技行业/智能手机","tax_ind_robot","机器人","Robotics","科技行业/机器人","tax_ind_wearable","智能穿戴","Smart Wearables","科技行业/智能穿戴","tax_ind_energy","新能源与智能制造","New Energy & Smart Manufacturing","科技行业/新能源与智能制造","tax_ind_biotech","生物科技","Biotech","科技行业/生物科技","tax_ind_quantum","量子计算","Quantum Computing","科技行业/量子计算","tax_ind_blockchain","区块链",[236],"Blockchain","科技行业/区块链","Web3","tax_ind_enterprise","企业软件","Enterprise Software","科技行业/企业软件","tax_ind_security","网络安全","Cybersecurity","科技行业/网络安全","tax_ind_semi","半导体",[250],"Semiconductor","科技行业/半导体","芯片","tax_ind_cloud","云计算","Cloud Computing","科技行业/云计算","tax_ind_ai","人工智能",[260,261],"Artificial Intelligence","科技行业/人工智能","AI","AI 技术","env",{"_264":24},"SITE_BASE_URL"]

Error-Correcting Codes in Projective Space 论文

Error-Correcting Codes in Projective Space · 相关技术

相关技术