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Reeds–Sloane Algorithm
The Reeds–Sloane algorithm, named after James Reeds and Neil Sloane, is an extension of the Berlekamp–Massey algorithm, an algorithm for finding the shortest linear-feedback shift register (LFSR) for a given output sequence, for use on sequences that take their values from the integers mod ''n''. References * External links Reeds–Sloane Algorithmon MathWorld ''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Dig ... Cryptanalytic algorithms {{crypto-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Reeds
James is a common English language surname and given name: *James (name), the typically masculine first name James * James (surname), various people with the last name James James or James City may also refer to: People * King James (other), various kings named James * Saint James (other) * James (musician) * James, brother of Jesus Places Canada * James Bay, a large body of water * James, Ontario United Kingdom * James College, York, James College, a college of the University of York United States * James, Georgia, an unincorporated community * James, Iowa, an unincorporated community * James City, North Carolina * James City County, Virginia ** James City (Virginia Company) ** James City Shire * James City, Pennsylvania * St. James City, Florida Arts, entertainment, and media * James (2005 film), ''James'' (2005 film), a Bollywood film * James (2008 film), ''James'' (2008 film), an Irish short film * James (2022 film), ''James'' (2022 film), an Indian Kannada ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neil Sloane
__NOTOC__ Neil James Alexander Sloane (born October 10, 1939) is a British-American mathematician. His major contributions are in the fields of combinatorics, error-correcting codes, and sphere packing. Sloane is best known for being the creator and maintainer of the On-Line Encyclopedia of Integer Sequences (OEIS). Biography Sloane was born in Beaumaris, Anglesey, Wales, in 1939, moving to Cowes, Isle of Wight, England in 1946. The family emigrated to Australia, arriving at the start of 1949. Sloane then moved from Melbourne to the United States in 1961. He studied at Cornell University under Nick DeClaris, Frank Rosenblatt, Frederick Jelinek and Wolfgang Heinrich Johannes Fuchs, receiving his Ph.D. in 1967. His doctoral dissertation was titled ''Lengths of Cycle Times in Random Neural Networks''. Sloane joined AT&T Bell Labs in 1968 and retired from AT&T Labs in 2012. He became an AT&T Fellow in 1998. He is also a Fellow of the Learned Society of Wales, an IEEE Fellow, a ... [...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 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 ... recognized its application to linear feedback shift registers and simplified the algorithm. Massey termed the algorithm the LFSR Synthesis Algorithm (Berlekamp Iterative Algorithm), but ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear-feedback Shift Register
In computing, a linear-feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state. The most commonly used linear function of single bits is exclusive-or (XOR). Thus, an LFSR is most often a shift register whose input bit is driven by the XOR of some bits of the overall shift register value. The initial value of the LFSR is called the seed, and because the operation of the register is deterministic, the stream of values produced by the register is completely determined by its current (or previous) state. Likewise, because the register has a finite number of possible states, it must eventually enter a repeating cycle. However, an LFSR with a well-chosen feedback function can produce a sequence of bits that appears random and has a very long cycle. Applications of LFSRs include generating pseudo-random numbers, pseudo-noise sequences, fast digital counters, and whitening sequences. Both hardware and software implementations o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called the ''length'' of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position. The notion of a sequence can be generalized to an indexed family, defined as a function from an ''arbitrary'' index set. For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be ''finite'', as in these examples, or ''infi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integers Mod N
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book ''Disquisitiones Arithmeticae'', published in 1801. A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00. Simple addition would result in , but clocks "wrap around" every 12 hours. Because the hour number starts over at zero when it reaches 12, this is arithmetic ''modulo'' 12. In terms of the definition below, 15 is ''congruent'' to 3 modulo 12, so "15:00" on a 24-hour clock is displayed "3:00" on a 12-hour clock. Congruence Given an integer , called a modulus, two integers and are said to be congruent modulo , if is a divisor of their difference (that is, if there is an integer such that ). Congruence modul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MathWorld
''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Digital Library grant to the University of Illinois at Urbana–Champaign. History Eric W. Weisstein, the creator of the site, was a physics and astronomy student who got into the habit of writing notes on his mathematical readings. In 1995 he put his notes online and called it "Eric's Treasure Trove of Mathematics." It contained hundreds of pages/articles, covering a wide range of mathematical topics. The site became popular as an extensive single resource on mathematics on the web. Weisstein continuously improved the notes and accepted corrections and comments from online readers. In 1998, he made a contract with CRC Press and the contents of the site were published in print and CD-ROM form, titled "CRC Concise Encyclopedia of Mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
