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Reed–Solomon Error Correction
Reed–Solomon codes are a group of error-correcting codes that were introduced by Irving S. Reed and Gustave Solomon in 1960. They have many applications, the most prominent of which include consumer technologies such as MiniDiscs, CDs, DVDs, Blu-ray discs, QR codes, data transmission technologies such as DSL and WiMAX, broadcast systems such as satellite communications, DVB and ATSC, and storage systems such as RAID 6. Reed–Solomon codes operate on a block of data treated as a set of finite-field elements called symbols. Reed–Solomon codes are able to detect and correct multiple symbol errors. By adding = − check symbols to the data, a Reed–Solomon code can detect (but not correct) any combination of up to erroneous symbols, ''or'' locate and correct up to erroneous symbols at unknown locations. As an erasure code, it can correct up to erasures at locations that are known and provided to the algorithm, or it can detect and correct combinations of e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Irving S
Irving may refer to: People *Irving (name), including a list of people with the name Fictional characters * Irving, the main character's love interest in Cathy (comic strip) * Lloyd Irving, the main protagonist in the ''Tales of Symphonia'' video game Places Canada * Irving Nature Park, a park in Saint John, N.B. United States *Irving, California, former name of Irvington, California * Irving, Illinois * Irving, Iowa * Irving (Duluth), Minnesota *Irving, New York * Irving, Texas * Irving, Wisconsin, a town ** Irving (community), Wisconsin, an unincorporated community *Irving Park, Chicago, Illinois * Irving Township, Montgomery County, Illinois * Irving Township, Michigan * Irving Township, Minnesota * Lake Irving, a lake in Minnesota Companies * Irving Group of Companies, Canadian conglomerate based in Saint John, New Brunswick, controlled by the Irving family, including: ** J. D. Irving, a conglomerate with holdings in forestry, pulp and paper, tissue, newsprint, buil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are given by the integers mod when is a prime number. The ''order'' of a finite field is its number of elements, which is either a prime number or a prime power. For every prime number and every positive integer there are fields of order p^k, all of which are isomorphic. Finite fields are fundamental in a number of areas of mathematics and computer science, including number theory, algebraic geometry, Galois theory, finite geometry, cryptography and coding theory. Properties A finite field is a finite set which is a field; this means that multiplication, addition, subtraction and division (excluding division by zero ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concatenated Error Correction Code
In coding theory, concatenated codes form a class of error-correcting codes that are derived by combining an inner code and an outer code. They were conceived in 1966 by Dave Forney as a solution to the problem of finding a code that has both exponentially decreasing error probability with increasing block length and polynomial-time decoding complexity. Concatenated codes became widely used in space communications in the 1970s. Background The field of channel coding is concerned with sending a stream of data at the highest possible rate over a given communications channel, and then decoding the original data reliably at the receiver, using encoding and decoding algorithms that are feasible to implement in a given technology. Shannon's channel coding theorem shows that over many common channels there exist channel coding schemes that are able to transmit data reliably at all rates R less than a certain threshold C, called the channel capacity of the given channel. In fact, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voyager Program
The Voyager program is an American scientific program that employs two robotic interstellar probes, ''Voyager 1'' and ''Voyager 2''. They were launched in 1977 to take advantage of a favorable alignment of Jupiter and Saturn, to fly near them while collecting data for transmission back to Earth. After launch the decision was taken to send ''Voyager 2'' near Uranus and Neptune to collect data for transmission back to Earth. As of 2022, the Voyagers are still in operation past the outer boundary of the heliosphere in interstellar space. They collect and transmit useful data to Earth. , ''Voyager 1'' was moving with a velocity of , or 17 km/s, relative to the Sun, and was from the Sun reaching a distance of from Earth as of February 10, 2022. On 25 August 2012, data from ''Voyager 1'' indicated that it had entered interstellar space. , ''Voyager 2'' was moving with a velocity of , or 15 km/s, relative to the Sun, and was from the Sun reaching a distance of from Ear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extended Euclidean Algorithm
In arithmetic and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common divisor (gcd) of integers ''a'' and ''b'', also the coefficients of Bézout's identity, which are integers ''x'' and ''y'' such that : ax + by = \gcd(a, b). This is a certifying algorithm, because the gcd is the only number that can simultaneously satisfy this equation and divide the inputs. It allows one to compute also, with almost no extra cost, the quotients of ''a'' and ''b'' by their greatest common divisor. also refers to a very similar algorithm for computing the polynomial greatest common divisor and the coefficients of Bézout's identity of two univariate polynomials. The extended Euclidean algorithm is particularly useful when ''a'' and ''b'' are coprime. With that provision, ''x'' is the modular multiplicative inverse of ''a'' modulo ''b'', and ''y'' is the modular multiplicative inverse of ''b'' mod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Massey
James Lee Massey (February 11, 1934 – June 16, 2013) was an American information theorist and cryptographer, Professor Emeritus of Digital Technology at ETH Zurich. His notable work includes the application of the Berlekamp–Massey algorithm to linear codes, the design of the block ciphers IDEA (with Xuejia Lai, based on the Lai-Massey scheme) and SAFER, and the Massey-Omura cryptosystem (with Jim K. Omura). Biography Massey was born in Wauseon, Ohio. As a child, after the death of his father in Ohio, he moved with his mother and brother to Mendota, Illinois. At age 14, his family moved to Ottawa, Illinois. After graduating from St. Bede Academy, he entered the University of Notre Dame. He received a B.S. in electrical engineering from Notre Dame in 1956 and was granted an NSF Fellowship. After three years of military service, he began graduate studies in 1959 at MIT, where he concentrated on coding theory and was awarded a Ph.D. in 1962, with John Wozencraft as his ad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elwyn Berlekamp
Elwyn Ralph Berlekamp (September 6, 1940 – April 9, 2019) was a professor of mathematics and computer science at the University of California, Berkeley.Contributors, ''IEEE Transactions on Information Theory'' 42, #3 (May 1996), p. 1048. DO10.1109/TIT.1996.490574Elwyn Berlekamp listing at the Department of Mathematics, . Berlekamp was widely known for his work in computer science, and |
Cyclic Code
In coding theory, a cyclic code is a block code, where the circular shifts of each codeword gives another word that belongs to the code. They are error-correcting codes that have algebraic properties that are convenient for efficient error detection and correction. Definition Let \mathcal be a linear code over a finite field (also called '' Galois field'') GF(q) of block length n. \mathcal is called a cyclic code if, for every codeword c=(c_1,\ldots,c_n) from \mathcal, the word (c_n,c_1,\ldots,c_) in GF(q)^n obtained by a cyclic right shift of components is again a codeword. Because one cyclic right shift is equal to n-1 cyclic left shifts, a cyclic code may also be defined via cyclic left shifts. Therefore the linear code \mathcal is cyclic precisely when it is invariant under all cyclic shifts. Cyclic codes have some additional structural constraint on the codes. They are based on Galois fields and because of their structural properties they are very useful for error control ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel Gorenstein
Daniel E. Gorenstein (January 1, 1923 – August 26, 1992) was an American mathematician. He earned his undergraduate and graduate degrees at Harvard University, where he earned his Ph.D. in 1950 under Oscar Zariski, introducing in his dissertation a duality principle for plane curves that motivated Grothendieck's introduction of Gorenstein rings. He was a major influence on the classification of finite simple groups. After teaching mathematics to military personnel at Harvard before earning his doctorate, Gorenstein held posts at Clark University and Northeastern University before he began teaching at Rutgers University in 1969, where he remained for the rest of his life. He was the founding director of DIMACS in 1989, and remained as its director until his death. Charles Weibel. Gorenst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BCH Codes
In coding theory, the Bose–Chaudhuri–Hocquenghem codes (BCH codes) form a class of cyclic error-correcting codes that are constructed using polynomials over a finite field (also called ''Galois field''). BCH codes were invented in 1959 by French mathematician Alexis Hocquenghem, and independently in 1960 by Raj Chandra Bose and D.K. Ray-Chaudhuri. The name ''Bose–Chaudhuri–Hocquenghem'' (and the acronym ''BCH'') arises from the initials of the inventors' surnames (mistakenly, in the case of Ray-Chaudhuri). One of the key features of BCH codes is that during code design, there is a precise control over the number of symbol errors correctable by the code. In particular, it is possible to design binary BCH codes that can correct multiple bit errors. Another advantage of BCH codes is the ease with which they can be decoded, namely, via an algebraic method known as syndrome decoding. This simplifies the design of the decoder for these codes, using small low-pow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MIT Lincoln Laboratory
The MIT Lincoln Laboratory, located in Lexington, Massachusetts, is a United States Department of Defense federally funded research and development center chartered to apply advanced technology to problems of national security. Research and development activities focus on long-term technology development as well as rapid system prototyping and demonstration. Its core competencies are in sensors, integrated sensing, signal processing for information extraction, decision-making support, and communications. These efforts are aligned within ten mission areas. The laboratory also maintains several field sites around the world. The laboratory transfers much of its advanced technology to government agencies, industry, and academia, and has launched more than 100 start-ups. History Origins At the urging of the United States Air Force, the Lincoln Laboratory was created in 1951 at the Massachusetts Institute of Technology (MIT) as part of an effort to improve the U.S. air defense syst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
