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- W4242875216 abstract "Error-correcting and error-detecting codes have their origins in the pioneering work of Hamming and Golay around 1950. The general theory is closely connected to topics in combinatorics and statistics such as block designs, which are discussed in this chapter. With error-detection, the receiver can tell if there has been a transmission error (or errors) but may not be able to correct the errors. Usually, however the receiver can ask for a re-send. This is the case for example with TCP and CRC protocols on the Internet. Although Hadamard matrices are firmly grounded in Euclidean geometry (from Hadamard’s theorem), the next construction considered in this chapter involves the more exotic world of finite fields. Reed–Muller codes are the simplest examples of the class of geometrical codes which also includes Euclidean geometry and projective geometry codes, all of which can be decoded by majority logic." @default.
- W4242875216 created "2022-05-12" @default.
- W4242875216 date "2021-07-14" @default.
- W4242875216 modified "2023-09-24" @default.
- W4242875216 title "Error‐Correction, Hadamard, and Bruen–Ott" @default.
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- W4242875216 doi "https://doi.org/10.1002/9781119582397.ch18" @default.
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