Abstract
Reed—Muller (RM) codes are a class of low-rate codes that have been largely replaced by Reed—Solomon codes. However, they have certain attributes which may well see their re-emergence in modern applications. In particular, coding and decoding is very fast. With Hamming codes (and the CRC used for correction), the message size was n bits where n = 2r − 1 and r was the number of redundant bits. Reed—Muller codes are based on maximal length codes which are, in some ways, the opposite of Hamming codes. Taking a typical Hamming code, say (15, 11), with four redundancy bits, the corresponding maximal length code would be a (15, 4) code so now, n = 2k − 1 and k is the number of information bits. This gives a very low coding rate of about 0.27.
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© 2001 Springer Science+Business Media New York
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Houghton, A. (2001). Reed-Muller Codes. In: Error Coding for Engineers. The Springer International Series in Engineering and Computer Science, vol 641. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1509-8_6
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DOI: https://doi.org/10.1007/978-1-4615-1509-8_6
Publisher Name: Springer, Boston, MA
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