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It provides the only known family of optimal (with respect to family size) OOCs having lambda =2. The parameters (n, omega , lambda ) are respectively (p/sup 2m/-1, p/sup m/+1,2), where p is any prime and the family size is p/sup m/-2. Three distinct upper bounds on the size of an OOC are presented that, for many values of the parameter set (n, omega , lambda ), improve upon the tightest previously known bound.< >","publishedDate","1990-07-01","publishedYear",1990,"venue","IEEE Transactions on Information Theory",235,"authors","keywords",[184,185,186],"pdfUrl","topVenue","graph theory and CDMA systems","Coding theory and cryptography","Biochemical and Structural Characterization","paper_W2124899794","Explicit Space–Time Codes Achieving the Diversity–Multiplexing Gain Tradeoff","{\"openalex\":\"W2124899794\",\"doi\":\"10.1109/tit.2006.880037\"}","2026-05-21T16:12:53.453885299","2026-05-21T16:20:32.186556548","10.1109/tit.2006.880037","W2124899794","A recent result of Zheng and Tse states that over a quasi-static channel, there exists a fundamental tradeoff, referred to as the diversity–multiplexing gain (D-MG) tradeoff, between the spatial multiplexing gain and the diversity gain that can be simultaneously achieved by a space–time (ST) code. This tradeoff is precisely known in the case of independent and identically distributed (i.i.d.) Rayleigh fading, for $T geq n_t+n_r-1$ where $T$ is the number of time slots over which coding takes place and $n_t,n_r$ are the number of transmit and receive antennas, respectively. For $T ≪ n_t+n_r-1$ , only upper and lower bounds on the D-MG tradeoff are available. In this paper, we present a complete solution to the problem of explicitly constructing D-MG optimal ST codes, i.e., codes that achieve the D-MG tradeoff for any number of receive antennas. We do this by showing that for the square minimum-delay case when $T=n_t=n$ , cyclic-division-algebra (CDA)-based ST codes having the nonvanishing determinant property are D-MG optimal. While constructions of such codes were previously known for restricted values of $n$ , we provide here a construction for such codes that is valid for all $n$ . For the rectangular, $T ≫ n_t$ case, we present two general techniques for building D-MG-optimal rectangular ST codes from their square counterparts. A byproduct of our results establishes that the D-MG tradeoff for all $Tgeq n_t$ is the same as that previously known to hold for $T geq n_t + n_r -1$ .","2006-08-29",2006,283,[199,200,185],"Advanced Wireless Communication Techniques","Cooperative Communication and Network Coding","paper_W2050500290","Optimal linear codes with a local-error-correction property","{\"openalex\":\"W2050500290\",\"doi\":\"10.1109/isit.2012.6284028\"}","2026-05-21T03:57:20.192514921","2026-05-21T03:57:20.19243312","10.1109/isit.2012.6284028","W2050500290","Motivated by applications to distributed storage, Gopalan et al recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a parity-check equation associated with small Hamming weight, thereby enabling recovery of the message symbol by examining a small number of other code symbols. This notion is expanded to the case when all code symbols, not just the message symbols, are covered by such “local” parity. In this paper, we extend the results of Gopalan et. al. so as to permit recovery of an erased code symbol even in the presence of errors in local parity symbols. We present tight bounds on the minimum distance of such codes and exhibit codes that are optimal with respect to the local error-correction property. As a corollary, we obtain an upper bound on the minimum distance of a concatenated code.","2012-07-01",2012,302,[213,214,185],"Advanced Data Storage Technologies","Error Correcting Code Techniques","paper_W2032685643","Generalized bent functions and their properties","{\"openalex\":\"W2032685643\",\"doi\":\"10.1016/0097-3165(85)90049-4\"}","2026-05-16T13:41:53.460075464","2026-05-19T06:35:52.332094241","10.1016/0097-3165(85)90049-4","W2032685643","1985-09-01",1985,"Journal of Combinatorial Theory Series A",449,[185,184,227],"Cancer Mechanisms and Therapy","paper_W2038681062","The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes","{\"openalex\":\"W2038681062\",\"doi\":\"10.1109/18.312154\"}","2026-05-14T07:37:31.262505041","2026-05-21T10:35:21.201390962","10.1109/18.312154","W2038681062","Certain notorious nonlinear binary codes contain more codewords than any known linear code. These include the codes constructed by Nordstrom-Robinson (1967), Kerdock (1972), Preparata (1968), Goethals (1974), and Delsarte-Goethals (1975). It is shown here that all these codes can be very simply constructed as binary images under the Gray map of linear codes over Z/sub 4/, the integers mod 4 (although this requires a slight modification of the Preparata and Goethals codes). The construction implies that all these binary codes are distance invariant. Duality in the Z/sub 4/ domain implies that the binary images have dual weight distributions. The Kerdock and \"Preparata\" codes are duals over Z/sub 4/-and the Nordstrom-Robinson code is self-dual-which explains why their weight distributions are dual to each other. The Kerdock and \"Preparata\" codes are Z/sub 4/-analogues of first-order Reed-Muller and extended Hamming codes, respectively. All these codes are extended cyclic codes over Z/sub 4/, which greatly simplifies encoding and decoding. An algebraic hard-decision decoding algorithm is given for the \"Preparata\" code and a Hadamard-transform soft-decision decoding algorithm for the I(Kerdock code. Binary first- and second-order Reed-Muller codes are also linear over Z/sub 4/, but extended Hamming codes of length n/spl ges/32 and the Golay code are not. Using Z/sub 4/-linearity, a new family of distance regular graphs are constructed on the cosets of the \"Preparata\" code.< >","1994-03-01",1994,1408,[185,184,200],{"_60":241,"_62":242},[],[243],{"_65":244,"_67":245,"_69":246,"_71":247},1784874873342,{"_74":249,"_76":77,"_78":244,"_80":-5,"_81":26,"_82":26,"_83":26,"_84":-5,"_85":-5,"_86":87,"_35":88,"_89":90},[73,248],"[\"portal\",\"industries\"]","industries",[250,251,252,253,254,255,256,257,258,259,260,261],{"_15":323,"_29":324,"_31":-5,"_32":325,"_33":326,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":265,"_42":-5,"_44":-5,"_266":267,"_268":-5,"_269":77,"_270":271,"_272":327,"_274":26,"_275":87,"_276":26,"_277":-5,"_58":324,"_59":326},{"_15":319,"_29":320,"_31":-5,"_32":-5,"_33":321,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":265,"_42":-5,"_44":-5,"_266":267,"_268":-5,"_269":77,"_270":271,"_272":322,"_274":26,"_275":87,"_276":26,"_277":-5,"_58":320,"_59":321},{"_15":313,"_29":314,"_31":-5,"_32":315,"_33":316,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":265,"_42":-5,"_44":-5,"_266":267,"_268":-5,"_269":77,"_270":271,"_272":317,"_274":26,"_275":87,"_276":26,"_277":-5,"_58":314,"_59":316},{"_15":309,"_29":310,"_31":-5,"_32":-5,"_33":311,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":265,"_42":-5,"_44":-5,"_266":267,"_268":-5,"_269":77,"_270":271,"_272":312,"_274":26,"_275":87,"_276":26,"_277":-5,"_58":310,"_59":311},{"_15":305,"_29":306,"_31":-5,"_32":-5,"_33":307,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":265,"_42":-5,"_44":-5,"_266":267,"_268":-5,"_269":77,"_270":271,"_272":308,"_274":26,"_275":87,"_276":26,"_277":-5,"_58":306,"_59":307},{"_15":299,"_29":300,"_31":-5,"_32":301,"_33":302,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":265,"_42":-5,"_44":-5,"_266":267,"_268":-5,"_269":77,"_270":271,"_272":303,"_274":26,"_275":87,"_276":26,"_277":-5,"_58":300,"_59":302},{"_15":294,"_29":295,"_31":-5,"_32":-5,"_33":296,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":265,"_42":-5,"_44":-5,"_266":267,"_268":-5,"_269":77,"_270":271,"_272":297,"_274":26,"_275":298,"_276":26,"_277":-5,"_58":295,"_59":296},{"_15":290,"_29":291,"_31":-5,"_32":-5,"_33":292,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":265,"_42":-5,"_44":-5,"_266":267,"_268":-5,"_269":77,"_270":271,"_272":293,"_274":26,"_275":87,"_276":26,"_277":-5,"_58":291,"_59":292},{"_15":286,"_29":287,"_31":-5,"_32":-5,"_33":288,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":265,"_42":-5,"_44":-5,"_266":267,"_268":-5,"_269":77,"_270":271,"_272":289,"_274":26,"_275":87,"_276":26,"_277":-5,"_58":287,"_59":288},{"_15":282,"_29":283,"_31":-5,"_32":-5,"_33":284,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":265,"_42":-5,"_44":-5,"_266":267,"_268":-5,"_269":77,"_270":271,"_272":285,"_274":26,"_275":87,"_276":26,"_277":-5,"_58":283,"_59":284},{"_15":278,"_29":279,"_31":-5,"_32":-5,"_33":280,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":265,"_42":-5,"_44":-5,"_266":267,"_268":-5,"_269":77,"_270":271,"_272":281,"_274":26,"_275":87,"_276":26,"_277":-5,"_58":279,"_59":280},{"_15":262,"_29":263,"_31":-5,"_32":-5,"_33":264,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":265,"_42":-5,"_44":-5,"_266":267,"_268":-5,"_269":77,"_270":271,"_272":273,"_274":26,"_275":87,"_276":26,"_277":-5,"_58":263,"_59":264},"tax_ind_smartphone","智能手机","Smartphone","manual","taxonomyType","INDUSTRY","code","level","parentId","tax_ind_root","path","科技行业/智能手机","sortOrder","isLeaf","entityCount","children","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",true,"tax_ind_blockchain","区块链",[304],"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",[318],"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",[328,329],"Artificial Intelligence","科技行业/人工智能","AI","AI 技术","env",{"_332":24},"SITE_BASE_URL"]

P. Vijay Kumar 人物

P. Vijay Kumar · 相关文章