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. [1]

5 天之前 · The Golay code is a perfect linear error-correcting code. There are two essentially distinct versions of the Golay code: a binary version and a ternary version. The binary version G_(23) is a (23,12,7) binary linear code consisting of 2^(12)=4096 codewords of length 23 and minimum distance 7.

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Marcel Jules Edouard Golay (French:; May 3, 1902 – April 27, 1989) was a Swiss mathematician, physicist, and information theorist, who applied mathematics to real-world military and industrial problems.

The connection described here between the Golay codes and the dodecahedron dates from the mid 80s. I originally described it using a cellular automaton with 13 cells, to wit, the 12 faces of a dodecahedron plus one cell consisting of its interior. Each cell …

2023年3月23日 · M.J.E. Golay (1902– 1989) was a Swiss physicist who worked in many different fields. He is known for his work on infrared spectroscopy and the invention of the capillary column, but to mathematicians mainly for his discovery of the two Golay codes.

2015年12月1日 · The extended binary Golay code, or extended Golay code for short, is the essentially unique way to encode 12 bits of data in a 24-bit word in such a way that errors affecting up to 3 bits can be corrected, and errors affecting up to 7 bits can at least be detected.