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Method in computational algebra
algebra, Berlekamp's algorithm is a well-known method for factoring polynomials over finite fields (also known as Galois fields). The algorithm consists
Berlekamp's_algorithm
Algorithm on linear-feedback shift registers
The Berlekamp–Massey algorithm is an algorithm that will find the shortest linear-feedback shift register (LFSR) for a given binary output sequence. The
Berlekamp–Massey_algorithm
Error-correcting 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
Berlekamp–Welch_algorithm
American mathematician (1940–2019)
Berkeley. Berlekamp was widely known for his work in computer science, coding theory and combinatorial game theory. Berlekamp invented an algorithm to factor
Elwyn_Berlekamp
computational algebra, the Berlekamp–Zassenhaus algorithm is an algorithm for factoring polynomials over the integers, named after Elwyn Berlekamp and Hans Zassenhaus
Berlekamp–Zassenhaus algorithm
Berlekamp–Zassenhaus_algorithm
Method in number theory
In number theory, Berlekamp's root finding algorithm, also called the Berlekamp–Rabin algorithm, is the probabilistic method of finding roots of polynomials
Berlekamp–Rabin_algorithm
is Berlekamp's algorithm, which combines stages 2 and 3. Berlekamp's algorithm is historically important as being the first factorization algorithm which
Factorization of polynomials over finite fields
Factorization_of_polynomials_over_finite_fields
modulo a prime number Berlekamp's root finding algorithm Cipolla's algorithm Tonelli–Shanks algorithm Multiplication algorithms: fast multiplication of
List_of_algorithms
Algorithm for factoring polynomials over finite fields
1981. It is arguably the dominant algorithm for solving the problem, having replaced the earlier Berlekamp's algorithm of 1967. It is currently implemented
Cantor–Zassenhaus_algorithm
American information theorist (1927–2023)
co-inventor of the Baum–Welch algorithm and the Berlekamp–Welch algorithm, also known as the Welch–Berlekamp algorithm. Welch received his B.S. in mathematics
Lloyd_R._Welch
Mathematical software
Gosper's algorithm Limit computation via e.g. Gruntz's algorithm Polynomial factorization via e.g., over finite fields, Berlekamp's algorithm or Cantor–Zassenhaus
Computer_algebra_system
version of the algorithms for list decoding RS codes - the Berlekamp–Welch algorithm. Welch and Berlekamp initially came with an algorithm which can solve
Guruswami–Sudan list decoding algorithm
Guruswami–Sudan_list_decoding_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
Reeds–Sloane_algorithm
Algorithm for computing greatest common divisors
In mathematics, the Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers
Euclidean_algorithm
Decomposition of a number into a product
efficient non-quantum integer factorization algorithm is known. However, it has not been proven that such an algorithm does not exist. The presumed difficulty
Integer_factorization
Algorithm that employs a degree of randomness as part of its logic or procedure
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random
Randomized_algorithm
Error-correcting codes
decoder was developed by Elwyn Berlekamp and James Massey and has since been known as the Berlekamp–Massey decoding algorithm. In 1975, another improved BCH
Reed–Solomon_error_correction
Way of calculating the day of the week of a given date
The Doomsday rule, Doomsday algorithm or Doomsday method is an algorithm of determination of the day of the week for a given date. It provides a perpetual
Doomsday_rule
proofs. A simple example of a non-constructive algorithm was published in 1982 by Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy, in their book
Non-constructive algorithm existence proofs
Non-constructive_algorithm_existence_proofs
efficient algorithm for decoding concatenated codes, which is based on using an errors-and-erasures decoder for the outer code. A naive decoding algorithm for
Generalized minimum-distance decoding
Generalized_minimum-distance_decoding
cube-solving algorithm. Later, Singmaster reported that Elwyn Berlekamp, John Conway, and Richard K. Guy had come up with a different algorithm that took
Optimal solutions for the Rubik's Cube
Optimal_solutions_for_the_Rubik's_Cube
Error correction code
popular algorithms for this task are: Peterson–Gorenstein–Zierler algorithm Berlekamp–Massey algorithm Sugiyama Euclidean algorithm Peterson's algorithm is
BCH_code
Type of error-correcting codes
is a Welch–Berlekamp-style interpolation (because it can be viewed as the higher-dimensional generalization of the Welch–Berlekamp algorithm). Suppose
Folded_Reed–Solomon_code
Algorithm for computing kernel vectors
{\displaystyle S} and hence S y {\displaystyle S_{y}} . But the Berlekamp–Massey algorithm allows us to calculate relatively efficiently some sequence q
Block_Wiedemann_algorithm
Well-spaced set of points in a metric space
errors. An example is provided by the Berlekamp switching game. Har-Peled & Raichel (2013) describe an algorithmic paradigm that they call "net and prune"
Delone_set
Algorithm for factorization of polynomials
notation). This is an improvement of both Berlekamp's algorithm and Rónyai's algorithm in the sense that the first algorithm is polynomial for small characteristic
Evdokimov's_algorithm
American information theorist, cryptographer, and scholar (1934 – 2013)
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
James_Massey
Asymmetric encryption algorithm developed by Robert McEliece
encryption algorithm developed in 1978 by Robert McEliece. It was the first such scheme to use randomization in the encryption process. The algorithm has never
McEliece_cryptosystem
Italian-American engineer and businessman
and businessman who co-founded Qualcomm Inc. and invented the Viterbi algorithm. He is the Presidential Chair Professor of Electrical Engineering at the
Andrew_Viterbi
Mathematical game
The Berlekamp switching game is a mathematical game proposed by American mathematician Elwyn Berlekamp. It has also been called the Gale–Berlekamp switching
Berlekamp_switching_game
Method of partitioning data points into groups based on their similarity
that the above algorithm is a 3-approximation algorithm for correlation clustering. The best polynomial-time approximation algorithm known at the moment
Correlation_clustering
Two-dimensional cellular automaton
programs often do not store cells as a two-dimensional arrays, instead using algorithms such as Hashlife which represent patterns as a tree structure. The Game
Conway's_Game_of_Life
converse is not necessarily true. Grantham's stated goal when developing the algorithm was to provide a test that primes would always pass and composites would
Quadratic_Frobenius_test
American quantitative hedge fund
a cryptanalyst from IDA who was also the co-author of the Baum–Welch algorithm. When Baum abandoned the idea of trading with mathematical models and
Renaissance_Technologies
1995 electronic game
Corresponding lights (see table below) in the top row are toggled and the initial algorithm is run again, resulting in a solution. □ - An activated lamp. ■ - A deactivated
Lights_Out_(game)
English mathematician (1937–2020)
For calculating the day of the week, he invented the Doomsday algorithm. The algorithm is simple enough for anyone with basic arithmetic ability to do
John_Horton_Conway
Italian computer scientist
recent being the notion of "algorithmic degree" as a key feature to control robust implementations of geometric algorithms. In addition, Preparata has
Franco_P._Preparata
Unsolved problem in computational complexity theory
subexponential time approximation algorithm for the unique games problem. A key ingredient in their result was the spectral algorithm of Alexandra Kolla (see also
Unique_games_conjecture
Question in combinatorial game theory
conditions. Oddvar Kloster discovered a constructive algorithm to solve the problem with a 2-angel. This algorithm is quite simple and also optimal, since, as
Angel_problem
Problem of sorting pairs of numbers by their sum
fastest known algorithm for X + Y {\displaystyle X+Y} sorting. Whether a faster algorithm exists is an open problem, posed by Elwyn Berlekamp prior to 1975
X_+_Y_sorting
the Viterbi algorithm, making decoding of convolutional codes practicable 1968 – Elwyn Berlekamp invents the Berlekamp–Massey algorithm; its application
Timeline of information theory
Timeline_of_information_theory
Israeli mathematician and computer scientist (1931–2026)
one of the most well-known efficient string search algorithms, the Rabin–Karp string search algorithm, known for its rolling hash. Rabin's subsequent research
Michael_O._Rabin
American scientist (1923–1965)
Mathematician and game theorist Elwyn Berlekamp, once an assistant to Kelly at Bell Labs, had applied the same logical algorithm for Axcom Trading Advisors, an
John_Larry_Kelly_Jr.
On existence of a strongly regular graph
2026 (link) Cameron, Peter J. (1994), Combinatorics: topics, techniques, algorithms, Cambridge: Cambridge University Press, p. 331, ISBN 0-521-45133-7, MR 1311922
Conway's_99-graph_problem
Kind of error correction code
rows. Decoding of binary Goppa codes is traditionally done by Patterson algorithm, which gives good error-correcting capability (it corrects all t {\displaystyle
Binary_Goppa_code
Abstract strategy game
Prencipe, Giuseppe (eds.), Proc. 9th International Conference on Fun with Algorithms (FUN 2018), Leibniz International Proceedings in Informatics (LIPIcs)
Subtraction_game
Three raised to an integer power
sets of an n-vertex graph, and in the time analysis of the Bron–Kerbosch algorithm for finding these sets. Several important strongly regular graphs also
Power_of_three
German mathematician (1912–1991)
ISBN 978-0-521-59669-5. Cantor, David G.; Zassenhaus, Hans (April 1981), "A new algorithm for factoring polynomials over finite fields", Mathematics of Computation
Hans_Zassenhaus
Mathematical linear code
algorithms based on the Berlekamp–Massey–Sakata algorithm. Shojiro Sakata introduced this algorithm as an extension of the Berlekamp–Massey algorithm
Algebraic_geometry_code
American computer scientist
Engineering and Science (IDEaS) that she co-founded, director of the Algorithms and Randomness Center, and served as the ADVANCE Professor of Computing
Dana_Randall
Error-correcting code
in network coding. Linear code Reed–Solomon error correction Berlekamp–Massey algorithm Network coding Codes for which each input symbol is from a set
Rank_error-correcting_code
Pencil and paper map-coloring game
Games: 1 Demaine, Erik; Hearn, Robert (2001). "Playing Games with Algorithms: Algorithmic Combinatorial Game Theory". arXiv:cs/0106019v2. Winning Ways: 2
Col_(game)
Linear error correcting code
adaptability to the iterative belief-propagation decoding algorithm. Under this algorithm, they can be designed to approach theoretical limits (capacities)
Low-density_parity-check_code
a variant of the Euclidean algorithm when N is prime; and in general by Xu's adaptation of the Berlekamp-Massey algorithm. If L is the size of the smallest
Feedback with Carry Shift Registers
Feedback_with_Carry_Shift_Registers
Mathematical game
In 2010, Julien Lemoine and Simon Viennot applied to the game of Cram algorithms that were initially developed for the game of Sprouts. It allowed them
Cram_(game)
Branch of game theory about two-player sequential games with perfect information
distinction in emphasis: while economic game theory tends to focus on practical algorithms—such as the alpha–beta pruning strategy commonly taught in AI courses—combinatorial
Combinatorial_game_theory
coding (LPC), a form of speech coding. In 1968, Elwyn Berlekamp invents the Berlekamp–Massey algorithm; its application to decoding BCH and Reed–Solomon codes
History_of_information_theory
exists an algorithm for classifying the winning and losing moves from the initial position in the game of Sylver coinage, even though the algorithm itself
Dickson's_lemma
Type of shift register in computing
minimal size that simulates the intended receiver by using the Berlekamp-Massey algorithm. This LFSR can then be fed the intercepted stretch of output stream
Linear-feedback shift register
Linear-feedback_shift_register
French, German, and Israeli researcher in quantum computing
Computation: Theory and Applications and was jointly supervised by Elwyn Berlekamp and chemist K. Birgitta Whaley. She joined CNRS at the University of Paris-Sud
Julia_Kempe
Combinatorial game with jumping pieces
arXiv:0804.0640. doi:10.37236/554. MR 2788684. S2CID 35020735. Levitin, Anany (2011). "Toads and Frogs". Algorithmic Puzzles. Oxford University Press. p. 53.
Toads_and_Frogs
Paper-and-pencil mathematical game
year, Julien Lemoine and Simon Viennot reached 17 spots with complicated algorithms. They were able to extend their analysis up to 20 points in 2011. The
Sprouts_(game)
enciphering algorithms, the asymmetric key algorithms. Prior to that time, all useful modern encryption algorithms had been symmetric key algorithms, in which
History_of_cryptography
Field of artificial intelligence around Go computer programs
programs even given handicaps of 10+ stones in favor of the AI. Many of the algorithms such as alpha-beta minimax that performed well as AIs for checkers and
Computer_Go
American electrical engineer (born 1931)
Gallager's research focus shifted to data networks, focusing on distributed algorithms, routing, congestion control, and random access techniques. In 1978, he
Robert_G._Gallager
Moving pattern in Conway's Game of Life
universal constructor that starts with only 15 gliders, with a construction algorithm published in 2022. Eric S. Raymond has proposed the glider as an emblem
Glider (Conway's Game of Life)
Glider_(Conway's_Game_of_Life)
American computer scientist known for Unix (born 1943)
variant of Thompson's notation. He also invented Thompson's construction algorithm used for converting regular expressions into nondeterministic finite automata
Ken_Thompson
Mathematical game
Nimbers". Journal of Algorithms. 43 (1): 106–119. doi:10.1006/jagm.2002.1215. Bodlaender, H.; Kratsch, D.; Timmer, S. (2015). "Exact algorithms for Kayles". Theoretical
Kayles
Adler-32 Algebraic geometry code BCH code BCJR algorithm Belief propagation Berger code Berlekamp–Massey algorithm Binary Golay code Binary Goppa code Bipolar
List of algebraic coding theory topics
List_of_algebraic_coding_theory_topics
Herman, Gabor T.; Kuba, Attila (eds.), Discrete tomography: Foundations, Algorithms, and Applications, Springer, pp. 85–114 Kasner, Edward (March 1903), "The
Midpoint_polygon
English mathematician and statistician
Sprague–Grundy theorems. The maximum number of colors used by a greedy coloring algorithm is called the Grundy number, also after this work on games, as its definition
Patrick_Michael_Grundy
ciphers • Beaufort cipher • Beaumanor Hall • Bent function • Berlekamp–Massey algorithm • Bernstein v. United States • BestCrypt • Biclique attack • BID/60
Index of cryptography articles
Index_of_cryptography_articles
Mathematics problem
the keys with the number 2, and the goat with the number 3. The basic algorithm is thus: Player 1 first opens door 1. If the car is behind the door, the
100_prisoners_problem
Board game for one player
Programming Based Algorithms for Peg Solitaire Problems", Proc. 2nd Int. Conf. Computers and Games (CG 2000): Integer programming based algorithms for peg solitaire
Peg_solitaire
Study of the properties of codes and their fitness
K. R. Rao in 1973. The DCT is the most widely used lossy compression algorithm, the basis for multimedia formats such as JPEG, MPEG and MP3. The aim
Coding_theory
Degenerate tic-tac toe variant
Generalization of the game Tic-tac-toe to higher dimensions "Game Theory and Algorithms Lecture 19: Nim & Impartial Combinatorial Games" (PDF). May 17, 2011.
Treblecross
Combinatorial game theory theorem
the field of combinatorial game theory, notably by Richard Guy, Elwyn Berlekamp, John Horton Conway and others, where they are now encapsulated in the
Sprague–Grundy_theorem
Points given to compensate for the disadvantage of playing second
19x19 grid for go, such as 7x7. When introducing Environmental Go, Elwyn Berlekamp made a broad generalisation of komi to illustrate the practical value
Komi_(Go)
Mental skill based games
a novel game designed by computer using evolutionary algorithms, demonstrating that algorithmic approaches could produce genuinely enjoyable games. Further
Abstract_strategy_game
simultaneous, and indeterminate equations. It also gave the modern standard algorithm for solving first-order diophantine equations. Jigu Suanjing (626 CE)
List of publications in mathematics
List_of_publications_in_mathematics
"his continuing contributions to the theory of algorithms including the development of efficient algorithms for network flow and other combinatorial optimization
List of University of California, Berkeley faculty
List_of_University_of_California,_Berkeley_faculty
Graph where every edge is in one triangle
MR 1761910 McKay, Brendan D.; Megill, Norman D.; Pavičić, Mladen (2000), "Algorithms for Greechie diagrams", International Journal of Theoretical Physics,
Locally_linear_graph
American mathematics and science writer (1914–2010)
majority of secure data transmission schemes. Since RSA is a relatively slow algorithm it is not widely used to directly encrypt data. More often, it is used
Martin_Gardner
American mathematician and educator (1921–2008)
mathematics teaching emphasizing understanding of concepts over rote algorithms. Gleason was "always interested in how people learn"; as part of the New
Andrew_M._Gleason
number, a representation as a sum of unit fractions found by a greedy algorithm. Sylvester's rank inequality rank(A) + rank(B) − n ≤ rank(AB) on the rank
List of things named after James Joseph Sylvester
List_of_things_named_after_James_Joseph_Sylvester
impossible. Environmental Go, also called Coupon Go, invented by Elwyn Berlekamp, adds an element of mathematical precision to the game by compelling players
Go_variants
BERLEKAMPS ALGORITHM
BERLEKAMPS ALGORITHM
BERLEKAMPS ALGORITHM
BERLEKAMPS ALGORITHM
Boy/Male
Tamil
Behavior
Boy/Male
Indian
Another name of God, Pile, Treasury
Boy/Male
Indian, Punjabi, Sikh
Infinite Fosterer
Male
Chamoru
, fiery, hot, passionate.
Surname or Lastname
English
English : occupational name for a net-maker, from an agent derivative of Middle English net ‘net’.English : variant of Nettard, an occupational name for a cattle herd, from Middle English neat ‘cattle’ + hi(e)rde ‘herdsman’.German : variant of Nader.German : habitational name for someone from any of various places called Nette, for example in Lower Saxony and Westphalia.Jewish (Ashkenazic) : unexplained.
Surname or Lastname
English
English : habitational name from either of two places in North Yorkshire called Helmsley. The names are of different etymologies: the one near Rievaulx Abbey is from the Old English personal name Helm + Old English lēah ‘wood’, ‘clearing’, whereas Upper Helmsley, near York, is from the Old English personal name Hemele + Old English ēg ‘island’, and had the form Hemelsey till at least the 14th century.
Girl/Female
Hindu, Indian, Tamil
Clarity
Boy/Male
Arabic, Muslim
Corpulent; A Distinguished Companion
Boy/Male
Bengali, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Handsome
Male
English
Variant spelling of English Barry, BARRIE means "fair-headed."
BERLEKAMPS ALGORITHM
BERLEKAMPS ALGORITHM
BERLEKAMPS ALGORITHM
BERLEKAMPS ALGORITHM
BERLEKAMPS ALGORITHM
n.
The art of calculating by nine figures and zero.
n.
Alt. of Algorithm
n.
The art of calculating with any species of notation; as, the algorithms of fractions, proportions, surds, etc.