Early information theory and Hamming codes were developed about 1950, but awaited technical innovations in data transmission and storage to be put to full use.
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One strategy for solving this version of the hat problem employs Hamming codes, which are commonly used to detect and correct errors in data transmission.
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An additional 5 error correcting bits produce a 31-bit Hamming code that can correct single-bit errors or detect double-bit errors ( but not both ).
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The key thing about Hamming Codes that can be seen from visual inspection is that any given bit is included in a unique set of parity bits.
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If the basic Hamming code detects an error, but the overall parity says that there are an even number of errors, an uncorrectable 2-bit error has occurred.
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Extended Hamming codes achieve a Hamming distance of four, which allows the decoder to distinguish between when at most one one-bit error occurs and when any two-bit errors occur.
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Jacques Hadamard did not invent the code himself, but he defined Hadamard matrices around 1893, long before the first error-correcting code, the Hamming code, was developed in the 1940s.
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The Hamming distance is named after Richard Hamming, who introduced the concept in his fundamental paper on Hamming codes " Error detecting and error correcting codes " in 1950.
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This way, it is possible to increase the minimum distance of the Hamming code to 4, which allows the decoder to distinguish between single bit errors and two-bit errors.
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The development of the Hamming codes was recognized in 1996 by the Eduard Rheim Foundation of Germany, which presented Hamming with the $ 130, 000 Eduard Rheim Award for Achievement in Technology.
