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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, University of California, Berkeley. Berlekamp was widely known for his work in computer science, coding theory and combinatorial gam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlekamp–Massey Algorithm
The Berlekamp–Massey algorithm is an algorithm that will find the shortest linear-feedback shift register (LFSR) for a given binary output sequence. The algorithm will also find the minimal polynomial of a linearly recurrent sequence in an arbitrary field. The field requirement means that the Berlekamp–Massey algorithm requires all non-zero elements to have a multiplicative inverse. Reeds and Sloane offer an extension to handle a ring. Elwyn Berlekamp invented an algorithm for decoding Bose–Chaudhuri–Hocquenghem (BCH) codes. James Massey recognized its application to linear feedback shift registers and simplified the algorithm. Massey termed the algorithm the LFSR Synthesis Algorithm (Berlekamp Iterative Algorithm), but it is now known as the Berlekamp–Massey algorithm. Description of algorithm The Berlekamp–Massey algorithm is an alternative to the Reed–Solomon Peterson decoder for solving the set of linear equations. It can be summarized as finding the coeffic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 errors ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlekamp's Algorithm
In mathematics, particularly computational algebra, Berlekamp's algorithm is a well-known method for factoring polynomials over finite fields (also known as ''Galois fields''). The algorithm consists mainly of matrix reduction and polynomial GCD computations. It was invented by Elwyn Berlekamp in 1967. It was the dominant algorithm for solving the problem until the Cantor–Zassenhaus algorithm of 1981. It is currently implemented in many well-known computer algebra systems. Overview Berlekamp's algorithm takes as input a square-free polynomial f(x) (i.e. one with no repeated factors) of degree n with coefficients in a finite field \mathbb_q and gives as output a polynomial g(x) with coefficients in the same field such that g(x) divides f(x). The algorithm may then be applied recursively to these and subsequent divisors, until we find the decomposition of f(x) into powers of irreducible polynomials (recalling that the ring of polynomials over a finite field is a unique ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Game Theory
Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Study has been largely confined to two-player games that have a ''position'' that the players take turns changing in defined ways or ''moves'' to achieve a defined winning condition. Combinatorial game theory has not traditionally studied games of chance or those that use imperfect or incomplete information, favoring games that offer perfect information in which the state of the game and the set of available moves is always known by both players. However, as mathematical techniques advance, the types of game that can be mathematically analyzed expands, thus the boundaries of the field are ever changing. Scholars will generally define what they mean by a "game" at the beginning of a paper, and these definitions often vary as they are specific to the game being analyzed and are not meant to represent the entire scope of the field. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Renaissance Technologies
Renaissance Technologies LLC, also known as RenTech or RenTec, is an American hedge fund based in East Setauket, New York, on Long Island, which specializes in systematic trading using quantitative models derived from mathematical and statistical analysis. Their signature Medallion fund is famed for the best record in investing history. Renaissance was founded in 1982 by James Simons, a mathematician who formerly worked as a code breaker during the Cold War. In 1988, the firm established its most profitable portfolio, the Medallion Fund, which used an improved and expanded form of Leonard Baum's mathematical models, improved by algebraist James Ax, to explore correlations from which they could profit. Elwyn Berlekamp was instrumental in evolving trading to shorter-dated, pure systems driven decision-making. The hedge fund was named Medallion in honor of the math awards that Simons and Ax had won. Renaissance's flagship Medallion fund, which is run mostly for fund employe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlekamp–Welch Algorithm
The Berlekamp–Welch algorithm, also known as the Welch–Berlekamp algorithm, is named for Elwyn R. Berlekamp and Lloyd R. Welch. This is a decoder algorithm that efficiently corrects errors in Reed–Solomon codes for an RS(''n'', ''k''), code based on the Reed Solomon original view where a message m_1, \cdots, m_k is used as coefficients of a polynomial F(a_i) or used with Lagrange interpolation to generate the polynomial F(a_i) of degree < ''k'' for inputs and then is applied to to create an encoded codeword . The goal of the decoder is to recover the original encoding polynomial , using the known inputs and received codeword with possible errors. It also computes an error polynomial where corresponding to errors in the received codeword. |
Ken Thompson
Kenneth Lane Thompson (born February 4, 1943) is an American pioneer of computer science. Thompson worked at Bell Labs for most of his career where he designed and implemented the original Unix operating system. He also invented the B programming language, the direct predecessor to the C programming language, and was one of the creators and early developers of the Plan 9 operating system. Since 2006, Thompson has worked at Google, where he co-developed the Go programming language. Other notable contributions included his work on regular expressions and early computer text editors QED and ed, the definition of the UTF-8 encoding, and his work on computer chess that included the creation of endgame tablebases and the chess machine Belle. He won the Turing Award in 1983 with his long-term colleague Dennis Ritchie. Early life and education Thompson was born in New Orleans, Louisiana. When asked how he learned to program, Thompson stated, "I was always fascinated with logic an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dover, Ohio
Dover is a city in Tuscarawas County, Ohio, United States, along the Tuscarawas River. The population was 13,112 at the 2020 census. It is located approximately south of Cleveland, west of Pittsburgh, and northeast of the state capital of Columbus. It is a principal city of the New Philadelphia–Dover micropolitan area. History Originally named Canal Dover due to its location and origins along the Ohio and Erie Canal, the land was platted in 1807, with Christian Deardorff and Jesse Slingluff recognized as the founders. Beginning in 1815, the post office first began operation. Canal Dover incorporated as a village in 1842 and became a city under the Ohio municipal code of 1903. On February 12, 1916, the city officially changed its name to Dover. Geography Dover is located at (40.526545, -81.477769), along the Tuscarawas River, near the mouth of Sugar Creek. According to the United States Census Bureau, the city has a total area of , of which is land and is water. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Julia Kempe
Julia Kempe is a French, German, and Israeli researcher in quantum computing. She is currently the Director of the Center for Data Science at NYU and Professor at the Courant Institute Education and career Kempe was born in East Berlin, to a family of Russian descent. She moved to Austria in 1990, and did her undergraduate studies in mathematics and physics at the University of Vienna from 1992 to 1995, with a year as an exchange student in physics at the University of Technology Sydney. She then earned two Master of Advanced Studies (DEA) degrees in France: one in mathematics in 1996 from Pierre and Marie Curie University and another in 1997 in physics from the ''École normale supérieure''. She completed two doctorates in 2001. The dissertation for her Ph.D. in computer science from the ''École nationale supérieure des télécommunications'' was entitled ''Quantum Computing: Random Walks and Entanglement'', and was supervised by Gérard Cohen. Her second Ph.D., in mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coding Theory
Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and data storage. Codes are studied by various scientific disciplines—such as information theory, electrical engineering, mathematics, linguistics, and computer science—for the purpose of designing efficient and reliable data transmission methods. This typically involves the removal of redundancy and the correction or detection of errors in the transmitted data. There are four types of coding: # Data compression (or ''source coding'') # Error control (or ''channel coding'') # Cryptographic coding # Line coding Data compression attempts to remove unwanted redundancy from the data from a source in order to transmit it more efficiently. For example, ZIP data compression makes data files smaller, for purposes such as to reduce Internet traffic. Data compressio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
