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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
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
Topics referred to by the same term
a data structure in computer science Ternary Golay code, a perfect [11, 6, 5] ternary linear code ?:, a ternary conditional operator used for basic conditional
Ternary
Topics referred to by the same term
error-correcting code Ternary Golay code, an error-correcting code Places: Golay, Kutch, a village in Kutch, Gujarat, India Gola (disambiguation) Golay code (disambiguation)
Golay
24-dimensional repeating pattern of points
the 1s of any codeword of the Golay code, and the ∓3 can appear in any position. The ternary Golay code, binary Golay code, and Leech lattice give very
Leech_lattice
Pairs of sequences
(also called maximum-length sequences or M-sequences) Ternary Golay code (Error-correcting code) Walsh-Hadamard sequences Zadoff–Chu sequence Donato,
Complementary_sequences
Study of the properties of codes and their fitness
1, 2r – 1 – r, 3), and the [23,12,7] binary and [11,6,5] ternary Golay codes. Another code property is the number of neighbors that a single codeword
Coding_theory
Mathematical tool
function for the Mathieu group M12 and ternary Golay code as the Miracle Octad Generator does for M24 and binary Golay code, respectively. Instead of using a
Miracle_Octad_Generator
Sporadic simple group
cover 2.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
Prakash, Shiroman (September 2020). "Magic state distillation with the ternary Golay code". Proceedings of the Royal Society A: Mathematical, Physical and Engineering
Magic_state_distillation
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 Voyager
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
Berlekamp–Van Lint–Seidel graph
Berlekamp–Van_Lint–Seidel_graph
{\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
Type of block code
Binary Golay code Cyclic redundancy check Eugene Prange Reed–Muller code Ternary Golay code Van Lint 1998, p. 76 Ryan & Lin 2009, pp. 108–109 Van Lint 1998
Cyclic_code
J. J. (1973), "A strongly regular graph derived from the perfect ternary Golay code" (PDF), in J.N. Srivastava (ed.), A Survey of Combinatorial Theory
Games_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
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
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
Logic puzzle
of 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
Graph where every edge is in one triangle
J. 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
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
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)
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)
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
Central computer component that executes instructions
employed more unusual representations such as bi-quinary coded decimal (base 2–5) or ternary (base 3). Nearly all modern CPUs represent numbers in binary
Central_processing_unit
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