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The binary Golay code, G 23 is a perfect code. That is, the spheres of radius three around code words form a partition of the vector space. G 23 is a 12-dimensional subspace of the space F 23 2. The automorphism group of the perfect binary Golay code G 23 (meaning the subgroup of the group S 23 of permutations of the coordinates of F 23
The code generally known simply as the ternary Golay code is an -code, that is, it is a linear code over a ternary alphabet; the relative distance of the code is as large as it possibly can be for a ternary code, and hence, the ternary Golay code is a perfect code. The extended ternary Golay code is a [12, 6, 6] linear code obtained by adding a ...
The Golay code, together with the related Witt design, features in a construction for the 196560 minimal vectors in the Leech lattice. Leech lattice (L mod 8) can be directly constructed by combination of the 3 following sets, = (+) + , (is a ones vector of size n), G - 24-bit Golay code; B - Binary integer sequence
The code word of the empty string is the empty string itself: ... and the [23,12,7] binary and [11,6,5] ternary Golay codes. ...
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 probes, and led to advances in the theory of finite groups. Co-author with Abraham Savitzky of the Savitzky–Golay filter. Inventor of the Golay cell, a type of infrared detector.
A block code (specifically a Hamming code) where redundant bits are added as a block to the end of the initial message A continuous convolutional code where redundant bits are added continuously into the structure of the code word. The two main categories of ECC codes are block codes and convolutional codes.
An NEC pager, using POCSAG coding branded for the Skyper network. Radio-paging code No. 1 (usually and hereafter called POCSAG) is an asynchronous protocol used to transmit data to pagers. Its usual designation is an acronym of the P ost O ffice C ode S tandardisation A dvisory G roup, the name of the group that developed the code under the ...
The Hadamard code is a locally decodable code, which provides a way to recover parts of the original message with high probability, while only looking at a small fraction of the received word. This gives rise to applications in computational complexity theory and particularly in the design of probabilistically checkable proofs .