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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,
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
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
Leech_lattice
Block design in combinatorial mathematics
the 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
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
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
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)
Five sporadic simple groups
The 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
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
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)
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
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
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
inventing 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
Coding_theory
Linear error correcting code
Gilbert–Varshamov bound for linear codes over binary fields with high probability. Over the binary erasure channel, code sequences were designed at rates
Low-density_parity-check_code
Type of error-correcting codes
1986, respectively. The binary lexicographic codes are linear codes, and include the Hamming codes and the binary Golay codes. A lexicode of length n
Lexicographic_code
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
Pairs of sequences
coefficients sum to zero. Binary complementary sequences were first introduced by Marcel J. E. Golay in 1949. In 1961–1962 Golay gave several methods for
Complementary_sequences
Error-correcting codes
Reed–Solomon code is usually a poor choice compared to a binary code. The Reed–Solomon code, like the convolutional code, is a transparent code. This means
Reed–Solomon_error_correction
High-performance forward error correction codes
Elke; Papke, Luiz (March 1996). "Iterative Decoding of Binary Block and Convolutional Codes" (PDF). IEEE Transactions on Information Theory. 42 (2):
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
The 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
Exceptional_object
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
{\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
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
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
can be corrected, the solution is essentially unique: the extended binary Golay code. Classification theorem Modulo, a mathematical term pertaining to
Essentially_unique
Swiss mathematician (1902–1989)
Discoverer of the famous binary and ternary Golay codes, which are perfect error-correcting codes that generalize the Hamming code. They were used in the
Marcel_J._E._Golay
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
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
Family of linear error-correcting codes
Hamming(7,4) code which adds three parity bits to four bits of data. In mathematical terms, Hamming codes are a class of binary linear codes. For each integer
Hamming_code
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
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
Open source amateur radio mode
(half-rate) modes. Three methods are used for error control: binary Golay code, punctured convolutional code and bit interleaving. Additionally, exclusive OR operation
M17_(amateur_radio)
Four finite groups derived from the Leech lattice
of 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
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
Electronic component
storage in capacitors to construct dynamic digital memories for the first binary computers that used electron tubes for logic. Pulsed power is used in many
Capacitor
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)
Algebraic structure
is 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 =
Moufang_loop
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
Near_polygon
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
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
Book
the 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
Central computer component that executes instructions
representations such as bi-quinary coded decimal (base 2–5) or ternary (base 3). Nearly all modern CPUs represent numbers in binary form, with each digit being
Central_processing_unit
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
Electronic circuits that utilize digital signals
devices that use or produce them. It deals with the relationship between binary inputs and outputs by passing electrical signals through logical gates,
Digital_electronics
Polynomial whose coefficients are all 1 or −1
approximate Hadamard matrices". Designs, Codes and Cryptography. 92: 3125–3131. doi:10.1007/s10623-024-01430-w. Golay, Marcel J. E. (1983). "The merit factor
Littlewood_polynomial
Vacuum tube with an electron beam deflectable to one of two anodes
anode collected or passed the beam, producing current variations in binary code, one bit at a time. CK1414 Character generator monoscope for text mode
Beam_deflection_tube
Open conjecture that no real circulant Hadamard matrix has order greater than 4
matrices". Designs, Codes and Cryptography. 92: 3125–3131. doi:10.1007/s10623-024-01430-w. Turyn, Richard; Storer, John (1961). "On binary sequences". Proceedings
Ryser's conjecture on circulant Hadamard matrices
Ryser's_conjecture_on_circulant_Hadamard_matrices
Vacuum tube used to display images
Williams-Kilburn tube was a cathode ray tube used to electronically store binary data. It was used in computers of the 1940s as a random-access digital storage
Cathode_ray_tube
Array of logic gates that are reprogrammable
validation techniques. Once the design and validation process is complete, the binary file generated, typically using the FPGA vendor's proprietary software,
Field-programmable_gate_array
distribution – redirects to Luby transform code Somers' D Sørensen similarity index Spaghetti plot Sparse binary polynomial hashing Sparse PCA – sparse principal
List_of_statistics_articles
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