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In mathematics and electronics engineering, a 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 a particularly deep and interesting connection to the theory of finite sporadic groups in mathematics.
Used in a football pool with 11 games, the ternary Golay code corresponds to 729 bets and guarantees exactly one bet with at most 2 wrong outcomes. The set of codewords with Hamming weight 5 is a 3- (11,5,4) design . The generator matrix given by Golay (1949, Table 1.) is.
The binary Golay code, independently developed in 1949, is an application in coding theory. More specifically, it is an error-correcting code capable of correcting up to three errors in each 24-bit word, and detecting up to seven. It was used to communicate with the Voyager probes, as it is much more compact than the previously-used Hadamard code.
In mathematics, the Miracle Octad Generator, or MOG, is a mathematical tool introduced by Rob T. Curtis for studying the Mathieu groups, binary Golay code and Leech lattice. Description [ edit ] The Miracle Octad Generator is a 4x6 array of combinations describing any point in 24-dimensional space.
The 4096 codewords of 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 by many methods, such as generating all 24-bit binary strings in lexicographic order and discarding those that differ from some earlier one in fewer than 8 ...
Other examples of classical block codes include Golay, BCH, Multidimensional parity, and Hamming codes. Hamming ECC is commonly used to correct NAND flash memory errors. [6] This provides single-bit error correction and 2-bit error detection.