Reed-Muller Codes
DOI:
https://doi.org/10.35819/remat2020v6i1id3429Keywords:
Codes, Reed-Muller, Mariner 9Abstract
The Reed-Muller codes were discovered by David Eugene Muller and decoded by Irving Stoy Reed in 1954. Such codes belong to the linear code family and are widely used nowadays, mainly for their simple and efficient decoding algorithm. There are several ways to define Reed-Muller codes. In this work, we present, in a clear and simple way, a recursive definition for all Reed-Muller codes of order r \in N, denoted by R (r, m), where 0 <= r <= m, m \in N. Using this definition, we show the main parameters: length, number of elements and minimum distance of first-order Reed-Muller codes, R(1, m) for all m \in N. In addition, we present an application of the first-order codes in a National Aeronautics and Space Administration (NASA) space program.
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https://orcid.org/0000-0002-0893-7426
