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Type of linear error-correcting code
binary Golay code is a type of linear error-correcting code used in digital communications. The binary Golay code, along with the ternary Golay code, has
Binary_Golay_code
Topics referred to by the same term
Golay code may refer to: Binary Golay code, an error-correcting code used in digital communications Ternary Golay code (Golay) complementary sequences
Golay_code
Pair of related error-correcting codes
In coding theory, the ternary Golay codes are two closely related error-correcting codes. The code generally known simply as the ternary Golay code is
Ternary_Golay_code
24-dimensional repeating pattern of points
The binary Golay code, independently developed in 1949, is an application in coding theory. More specifically, it is an error-correcting code capable of
Leech_lattice
Sporadic simple group
24 objects. (In coding theory the term "binary Golay code" often refers to a shorter related length 23 code, and the length 24 code used here is called
Mathieu_group_M24
Mathematical tool
tool introduced by Rob T. Curtis for studying the Mathieu groups, binary Golay code and Leech lattice. The Miracle Octad Generator is a 4x6 array of combinations
Miracle_Octad_Generator
Five sporadic simple groups
group M24 is the permutation automorphism group of the extended binary Golay code W, i.e., the group of permutations on the 24 coordinates that map W to
Mathieu_group
Topics referred to by the same term
Golay: Golay cell, a detector for infrared spectroscopy Savitzky–Golay filter, a signal processing filter Binary Golay code, an error-correcting code
Golay
Scheme for controlling errors in data over noisy communication channels
GPS etc. Berger code Constant-weight code Convolutional code Expander codes Group codes Golay codes, of which the Binary Golay code is of practical interest
Error_correction_code
Type of cyclic code
{\displaystyle (23,12)} binary Golay code over G F ( 2 ) {\displaystyle GF(2)} and the ( 11 , 6 ) {\displaystyle (11,6)} ternary Golay code over G F ( 3 ) {\displaystyle
Quadratic_residue_code
Block design in combinatorial mathematics
24-bit binary Golay code are generated, and the 759 codewords with a Hamming weight of 8 correspond to the S(5,8,24) system. The Golay code can be constructed
Steiner_system
Natural number
number 24 also occurs in coding theory and finite group theory through the extended binary Golay code, a self-dual binary linear code with parameters [ 24
24_(number)
Family of error-correcting codes that encode data in blocks
codes, Hadamard codes, Expander codes, Golay codes, Reed–Muller codes and Polar codes. These examples also belong to the class of linear codes, and hence they
Block_code
Study of the properties of codes and their fitness
the field of information theory. The binary Golay code was developed in 1949. It is an error-correcting code capable of correcting up to three errors in
Coding_theory
Family of linear error-correcting codes
error has occurred. Coding theory Gray code Golay code Hamming bound Hamming distance Low-density parity-check code Reed–Muller code Reed–Solomon error
Hamming_code
Algorithm to smooth data points
A Savitzky–Golay filter is a digital filter that can be applied to a set of digital data points for the purpose of smoothing the data, that is, to increase
Savitzky–Golay_filter
Natural number
vectors in the Leech lattice. The extended binary Golay code is an extension of the perfect binary Golay code B 23 {\displaystyle \mathbb {B} _{23}} , which
23_(number)
If the Hamming weight of all of a binary code's codewords is even
doubly even codes are the extended binary Hamming code of block length 8 and the extended binary Golay code of block length 24. These two codes are, in addition
Even_code
Type of error-correcting codes
respectively. The binary lexicographic codes are linear codes, and include the Hamming codes and the binary Golay codes. A lexicode of length n and minimum
Lexicographic_code
Communications protocol
and adoption of the POCSAG code, pagers used one of several codes such as binary Golay code. In the 1990s new paging codes were developed that offered
POCSAG
Linear error correcting code
(LDPC) codes, also known as Gallager codes, are a class of error-correction codes first proposed in 1960. Together with the closely related turbo codes, they
Low-density_parity-check_code
Error-correcting codes
In information theory and coding theory, Reed–Solomon codes are a group of error-correcting codes that were introduced by Irving S. Reed and Gustave Solomon
Reed–Solomon_error_correction
Sporadic simple group
relation, certain products of commuting involutions generate the binary Golay code, which extends to the maximal subgroup 211:M24. Bolt, Bray, and Curtis
Janko_group_J4
Pairs of sequences
Communications coded aperture masks are designed using a 2-dimensional generalization of complementary sequences. Binary Golay code (Error-correcting code) Gold
Complementary_sequences
Class of error-correcting code
linear code is a sequence of dual Hamming codes. Some examples of linear codes include: Repetition code Parity code Cyclic code Hamming code Golay code, both
Linear_code
System of rules to convert information into another form or representation
Bose–Chaudhuri–Hochquenghem, Turbo, Golay, algebraic geometry codes, low-density parity-check codes, and space–time codes. Error detecting codes can be optimised to detect
Code
High-performance forward error correction codes
In information theory, turbo codes are a class of high-performance forward error correction (FEC) codes developed around 1990–91, but first published in
Turbo_code
Type of block code
n. Multi-twisted codes are further generalizations of QT codes, which join multiple QT codes end to end. BCH code Binary Golay code Cyclic redundancy
Cyclic_code
Logic puzzle
the perfect ternary Golay code (Virtakallio-Golay code). At the same time, it is established that a static WA (i.e. weighting code) with the same parameters
Balance_puzzle
Swiss mathematician (1902–1989)
Marcel Jules Edouard Golay (French: [gɔlɛ]; May 3, 1902 – April 27, 1989) was a Swiss mathematician, physicist, and information theorist, who applied
Marcel_J._E._Golay
van Lint, and Johan Jacob Seidel [de] as the coset graph of the ternary Golay code. This graph is the Cayley graph of an abelian group. Among abelian Cayley
Berlekamp–Van Lint–Seidel graph
Berlekamp–Van_Lint–Seidel_graph
algorithm Binary Golay code Binary Goppa code Bipolar violation CRHF Casting out nines Check digit Chien's search Chipkill Cksum Coding gain Coding theory Constant-weight
List of algebraic coding theory topics
List_of_algebraic_coding_theory_topics
Four finite groups derived from the Leech lattice
Co0 with a subgroup he called N, a holomorph of the (extended) binary Golay code (as diagonal matrices with 1 or −1 as diagonal elements) by the Mathieu
Conway_group
be corrected, the solution is essentially unique: the extended binary Golay code. Classification theorem Modulo, a mathematical term pertaining to the
Essentially_unique
Topics referred to by the same term
heap, a data structure in computer science Ternary Golay code, a perfect [11, 6, 5] ternary linear code ?:, a ternary conditional operator used for basic
Ternary
codewords of the extended binary Golay code have a length of 24 bits and have weights 0, 8, 12, 16, or 24. This code can correct up to three errors. So
Exceptional_object
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
Concatenated error correction code
Concatenated_error_correction_code
Sequence of digital values used for synchronisation
Ohn; Asfis, Giorgos; Meng, Hongying (2019). "Convolution of Barker and Golay Codes for Low Voltage Ultrasonic Testing". Technologies. 7 (4): 72. doi:10
Barker_code
Arrangement of spheres within a space
linear codes. There are other, subtler relationships between Euclidean sphere packing and error-correcting codes. For example, the binary Golay code is closely
Sphere_packing
Sporadic simple group
M12 is the automorphism group of the extended ternary Golay code, a dimension 6 length 12 code over the field of order 3 of minimum weight 6. In particular
Mathieu_group_M12
Quantum computing algorithm
Shiroman (September 2020). "Magic state distillation with the ternary Golay code". Proceedings of the Royal Society A: Mathematical, Physical and Engineering
Magic_state_distillation
Algebraic structure
an elementary abelian group of order 212, identified with the binary Golay code. The loop is then defined up to isomorphism by the equations A2 = (−1)|A|/4
Moufang_loop
Limit on the parameters of a block code
codes. In 1973, Tietäväinen proved that any non-trivial perfect code over a prime-power alphabet has the parameters of a Hamming code or a Golay code
Hamming_bound
Book
binary Golay codes, and the ternary Golay codes. The second edition adds material on BCH codes, Reed–Solomon error correction, Reed–Muller codes, decoding
Introduction to the Theory of Error-Correcting Codes
Introduction_to_the_Theory_of_Error-Correcting_Codes
Electronic component
marking code for capacitors for very small parts which leave no room to print the above-mentioned three-/four-character code onto them. The code consists
Capacitor
Polyhedron with 24 faces
two) Archived 2016-03-04 at the Wayback Machine, David A. Richter The Golay Code on the Dodecadodecahedron Archived 2018-10-18 at the Wayback Machine,
Dodecadodecahedron
First NASA mission to orbit Jupiter (1989–2003)
subsystem bulk memory (DBUM), timing chains (TC), phase locked loops (PLL), Golay coders (GC), hardware command decoders (HCD) and critical controllers (CRC)
Galileo_(spacecraft)
Optoelectronic temperature sensing device
Code Correlation DTS sends on/off sequences of limited length into the fiber. The codes are chosen to have suitable properties, e.g. binary Golay code
Distributed temperature sensing
Distributed_temperature_sensing
Sporadic simple group
ISBN 978-0-387-98585-5, MR 0920369 Thompson, Thomas M. (1983), From error-correcting codes through sphere packings to simple groups, Carus Mathematical Monographs
Conway_group_Co1
British-canadian mathematician
"Moscow-Soicher Graph". Yet Another Distance Regular Graph Related to a Golay Code, Leonard H. Soicher, The Electronic Journal of Combinatorics, Volume 2
Leonard_Soicher
List of terms created from a person's name
scientist – Goethian, Goethite Marcel J.E. Golay, Swiss mathematician – Binary Golay code, Savitzky–Golay filter Rube Goldberg, American comics artist
List_of_eponyms_(A–K)
Shannon–Fano coding 1949 – Leon G. Kraft discovers Kraft's inequality, which shows the limits of prefix codes 1949 – Marcel J. E. Golay introduces Golay codes for
Timeline of information theory
Timeline_of_information_theory
Concept in incidence geometry
extended binary Golay code. It is constructed by taking the 759 octads (blocks) in the Witt design S(5, 8, 24) corresponding to the Golay code as points and
Near_polygon
Rudin–Shapiro sequence, also known as the Golay–Rudin–Shapiro sequence, is an infinite 2-automatic sequence named after Marcel Golay, Harold S. Shapiro, and Walter
Rudin–Shapiro_sequence
J. (1973), "A strongly regular graph derived from the perfect ternary Golay code" (PDF), in J.N. Srivastava (ed.), A Survey of Combinatorial Theory, Amsterdam:
Games_graph
Reliable digital data delivery methods on unreliable channels
concatenated with an outer Golay (24,12,8) code. The Voyager 2 craft additionally supported an implementation of a Reed–Solomon code. The concatenated Reed–Solomon–Viterbi
Error detection and correction
Error_detection_and_correction
Graph where every edge is in one triangle
J. (1973), "A strongly regular graph derived from the perfect ternary Golay code", A Survey of Combinatorial Theory (Proc. Internat. Sympos., Colorado
Locally_linear_graph
Passive electronic component providing electrical resistance
8186 / JIS C 5062 etc. (Resistor color code, RKM code, date code) EIA RS-279 / DIN 41429 (Resistor color code) IEC 60063 (IEC 63) / JIS C 5063 (Standard
Resistor
1988 mathematical book
stacking cannonballs. The interrelated topics featured in the book include Golay codes, Mathieu groups and Monstrous Moonshine. Many of the chapters are updates
Sphere Packings, Lattices and Groups
Sphere_Packings,_Lattices_and_Groups
Barker code, however, only has a single chipping sequence. The complementary codes first discussed by Golay were pairs of binary complementary codes and
Complementary_code_keying
Medication used to treat diabetes
trials". Obesity Reviews. 20 (1): 1–12. doi:10.1111/obr.12753. PMID 30230172. Golay A (January 2008). "Metformin and body weight". International Journal of
Metformin
Type of noise gate
same code as radios in the existing system. DCS adds a 134.4 bit/s (sub-audible) bitstream to the transmitted audio. The code word is a 23-bit Golay (23
Squelch
Moving average and polynomial regression method for smoothing data
meta-model. In some fields, LOESS is known and commonly referred to as Savitzky–Golay filter (proposed 15 years before LOESS). LOESS and LOWESS thus build on
Local_regression
Type of statistical measure over subsets of a dataset
least squares Rising moving average Rolling hash Running total Savitzky–Golay filter Window function Zero lag exponential moving average Hydrologic Variability
Moving_average
American software engineer (1936–2026)
May 26, 2019 – via Defense Technical Information Center. Ouyang, Meng; Golay, Michael W. (September 1995). An Integrated Formal Approach for Developing
Margaret Hamilton (software engineer)
Margaret_Hamilton_(software_engineer)
1985 Zimmerwald Schildknecht, T. EOS 18 km (11 mi) MPC · JPL 3329 Golay 1985 RT1 Golay September 12, 1985 Zimmerwald P. Wild EOS 18 km (11 mi) MPC · JPL
List of minor planets: 3001–4000
List_of_minor_planets:_3001–4000
Wireless telecommunications device
services personnel. Common paging protocols include TAP, FLEX, ReFLEX, POCSAG, GOLAY, ERMES and NTT. Past paging protocols include Two-tone and 5/6-tone. In
Pager
Swiss luxury watchmaker
Jaeger-LeCoultre) and Jules César Savary was named chairman of Audemars Piguet. Georges Golay also became the company's first executive from outside the founding families
Audemars_Piguet
Armed Philippine-American conflict (1899–1902)
323. Agoncillo 1990, p. 217. Zaide 1994, p. 279. Golay 1997, pp. 48, 49. Agoncillo 1990, p. 219, Golay 1997, pp. 49, 51. Worcester, D.C. (1900). Papers
Philippine–American_War
connector FAKRA connector is a modified SMB connector with a keyed and colour coded plastic housing and latch, used in the automotive industry SMC connector
List_of_RF_connector_types
School in Exeter, New Hampshire, US
department Frederick Buechner, minister and author Instructor in history Michael Golay, historian and author Instructor in English Todd Hearon, poet Instructor
Phillips_Exeter_Academy
Neurodevelopmental disorder
PMID 27189265. S2CID 7171541. Baggio S, Fructuoso A, Guimaraes M, Fois E, Golay D, Heller P, et al. (2 August 2018). "Prevalence of Attention Deficit Hyperactivity
Attention deficit hyperactivity disorder
Attention_deficit_hyperactivity_disorder
Steerable filters can be used for computing derivatives Moreover, Savitzky and Golay propose a least-squares polynomial smoothing approach, which could be used
Image_derivative
Electronic circuit formed on a small, flat piece of semiconductor material
represented as a two-digit year followed by a two-digit week code, such that a part bearing the code 8341 was manufactured in week 41 of 1983, or approximately
Integrated_circuit
Integral expressing the amount of overlap of one function as it is shifted over another
blurring. In digital data processing In analytical chemistry, Savitzky–Golay smoothing filters are used for the analysis of spectroscopic data. They
Convolution
Medical condition
Michaud-Feinberg, Joelle; Gutiérrez-Rojas, Luis; Zorzi, Carline; Klauser, Paul; Golay, Philippe; Kramer, Ueli; Alameda, Luis (June 2025). "Effectiveness of mindfulness
Mental_disorder
Connector used to connect to mains power
similar purposes – Types, basic parameters and dimensions (English Version)". Code of China. "Power plug & outlet Type O". WorldStandards.eu. 27 December 2024
AC_power_plugs_and_sockets
Clara University Scholar Commons. Retrieved November 4, 2021. Golay 1997, p. 49. Golay 1997, pp. 50–51. Seekins 1993 Kalaw 1927, p. 453Appendix F Zaide
History of the Philippines (1898–1946)
History_of_the_Philippines_(1898–1946)
Branch of medicine devoted to mental disorders
Michaud-Feinberg, Joelle; Gutiérrez-Rojas, Luis; Zorzi, Carline; Klauser, Paul; Golay, Philippe; Kramer, Ueli; Alameda, Luis (June 2025). "Effectiveness of mindfulness
Psychiatry
Solid-state electrically operated switch also used as an amplifier
with a letter (e.g. C often means high hFE, such as in: BC549C) or other codes may follow to show gain (e.g. BC327-25) or voltage rating (e.g. BUK854-800A)
Transistor
Treaty establishing the Philippines as an independent sovereign state
Past and Present (vol. 1 of 2)". Macmillan. Retrieved January 21, 2008. Golay 1997, pp. 49–50 Wertheim, Stephen (September 1, 2009). "Reluctant Liberator:
Treaty_of_Manila_(1946)
Type of resistor, usually with three terminals
"audio taper") potentiometers. A letter code may be used to identify which taper is used, but the letter code definitions are not standardized. Potentiometers
Potentiometer
Device that controls current between electrodes
quality of tubes. During the war Colossus was instrumental in breaking German codes. After the war, development continued with tube-based computers including
Vacuum_tube
Poisonous snake found in the Middle East
Hebrew). Society for the Protection of Nature in Israel. May 10, 2024. Golay P, Smith HM, Broadley DG [fr], Dixon JR, McCarthy CJ, Rage J-C, Schätti
Daboia_palaestinae
Vacuum tube used to display images
could be drawn by selecting the position on the mask corresponding to the code for a space (in practice, they were simply not drawn), which had a small
Cathode_ray_tube
Modeling language
Editorial Supplement, 8ES-24ES. Electronic Design, Apr. 1994. Ouyang, M., Golay, M.W. 1995, An Integrated Formal Approach for Developing High Quality Software
Universal_Systems_Language
Temperature control system
There are no standards for wiring color codes, but convention has settled on the following terminal codes and colors. In all cases, the manufacturer's
Thermostat
Central computer component that executes instructions
on (called operands), status information from previous operations, and a code from the control unit indicating which operation to perform. Depending on
Central_processing_unit
Open source amateur radio mode
(LICH) is encoded using the extended Golay (24,12) code. Stream contents are protected using a rate-1/2 convolutional code with puncturing, followed by bit
M17_(amateur_radio)
DC-DC voltage step-down power converter
control of digital buck converter Description and working VisSim source code diagram for low cost digital control of DC-DC buck converters SPICE simulation
Buck_converter
20th-century entertainment genre
tandem of Pugo and Togo, and Dolphy, who started under the stage name "Golay" as a comic dance partner of Bayani Casimiro. Many bodabil shows during
Vaudeville_in_the_Philippines
City in Switzerland
(1790–1863), Protestant divine Victor Gautier (1824–1890), Swiss physician Marcel Golay (1927–2015), astronomer Claude Goretta (1929–2019), film director and television
Geneva
1898–1902 U.S. military occupation of the Philippines
p. 318 Ch.28 Kalaw 1927, pp. 199–200 Ch.7 name="golay1997p49">Golay 1997, p. 49. Golay 1997, pp. 50–51. "The Philippines : As viewed by President McKinley's
Military Government of the Philippine Islands
Military_Government_of_the_Philippine_Islands
Two-terminal electronic component
European Pro Electron coding system for active components was introduced in 1966 and comprises two letters followed by the part code. The first letter represents
Diode
Spline function
curves. In a comparable study, the two-dimensional version of the Savitzky–Golay filtering and the spline method produced better results than moving average
B-spline
Quantum cascade detector (QCD) Resonant-cavity-enhanced photo detector (RCE) Golay cell Hybrid pixel detector Semiconductor detector Voltage regulators Linear
History_of_the_transistor
Electrical or optical connectors for carrying audio and video signals
1997–2001. PC 99 introduced a color code for the various standard types of plugs and connectors used on PCs. The color codes for audio plugs follow: † Though
Audio and video interfaces and connectors
Audio_and_video_interfaces_and_connectors
Type of field-effect transistor
Quantum cascade detector (QCD) Resonant-cavity-enhanced photo detector (RCE) Golay cell Hybrid pixel detector Semiconductor detector Voltage regulators Linear
MOSFET
Array of logic gates that are reprogrammable
power efficiencies that FPGAs provide. OpenCL allows programmers to develop code in the C programming language. For further information, see high-level synthesis
Field-programmable_gate_array
Method for producing electronic circuits
code. The same code marked on different packages or on devices from different manufacturers can translate to different devices. Many of these codes,
Surface-mount_technology
travel, tourism, insurance
GOLAY CODE
GOLAY CODE
GOLAY CODE
GOLAY CODE
GOLAY CODE
GOLAY CODE
GOLAY CODE
GOLAY CODE
GOLAY CODE
travel, tourism, insurance