computer science. Reed–Muller codes generalize the Reed–Solomon codes and the Walsh–Hadamard code. Reed–Muller codes are linear block codes that are locally...

Reed–Muller may refer to: Reed–Muller code Reed–Muller expansion This disambiguation page lists articles associated with the title Reed–Muller. If an internal...

information theory and coding theory, Reed–Solomon codes are a group of error-correcting codes that were introduced by Irving S. Reed and Gustave Solomon...

Locally decodable codes are especially useful for data transmission over noisy channels. The Hadamard code (a special case of Reed Muller codes) was used in...

Mexico. Muller C-element Reed–Muller code Reed–Muller expansion Muller's method (an established root finding method in numerical analysis) Muller automaton...

called the Hadamard code and it is the same as the first order Reed–Muller code over the binary alphabet. Normally, Hadamard codes are based on Sylvester's...

error-detecting codes known as Reed–Solomon codes in collaboration with Gustave Solomon. He also co-invented the Reed–Muller code. Reed made many contributions...

occurred. Coding theory Golay code Hamming bound Hamming distance Low-density parity-check code Reed–Muller code Reed–Solomon error correction Turbo code See...

correcting code Reed–Solomon error correction Reed–Muller code Repeat-accumulate code Repetition codes, such as Triple modular redundancy Spinal code, a rateless...

codes, of which BCH codes are an example Reed–Solomon codes Reed–Muller code Algebraic geometry code Binary Goppa code Low-density parity-check codes...

codes, Hadamard codes, Expander codes, Golay codes, Reed–Muller codes and Polar codes. These examples also belong to the class of linear codes, and hence they...

In Boolean logic, a Reed–Muller expansion (or Davio expansion) is a decomposition of a Boolean function. For a Boolean function f ( x 1 , … , x n ) :...

Instead of using a repetition code, a [32, 6, 16] Hadamard code was used, which is also a 1st-order Reed-Muller code. Errors of up to seven bits per...

the form of (sub-optimally decoded) convolutional codes and Reed–Muller codes. The Reed–Muller code was well suited to the noise the spacecraft was subject...

Reed–Muller code that had been used to transmit the black and white Mariner images was replaced with the much higher data rate Golay (24,12,8) code....

dimensions or length of messages of an error-correcting Reed-Muller code made of 64 block codes. The Global Positioning System (GPS) works on a ten-digit...

codes (e.g., BCH codes) Reed–Solomon codes Algebraic geometric codes Reed–Muller codes Perfect codes Locally recoverable code Block codes are tied to the...

almost directly be used as an error-correcting code using a Hadamard code (generalized in Reed–Muller codes), and are also used in balanced repeated replication...

variable-length code is uniquely decodable 1954 – Irving S. Reed and David E. Muller propose Reed–Muller codes 1955 – Peter Elias introduces convolutional codes 1957...

to QR codes. Reed Solomon Codes for Coders – an elaborate tutorial on Wikiversity, covering both QR code structure and the Reed Solomon codes used to...

of channel coding include: Parity checks Hamming code Reed-Muller code Reed-Solomon code Turbo coding See main article Line code Line coding consists of...

vectors of) lines of π. When π = AG(2, q) the geometric code generated is the q-ary Reed-Muller Code. Affine spaces can be defined in an analogous manner...

Binary Golay code Cyclic redundancy check Eugene Prange Reed–Muller code Ternary Golay code Van Lint 1998, p. 76 Van Lint 1998, p. 80 Hill 1988, pp. 159–160...

"Magic-State Distillation in All Prime Dimensions Using Quantum Reed-Muller Codes". Physical Review X. 2 (4): 041021. arXiv:1205.3104. Bibcode:2012PhRvX...

especially convenient way of expressing the Reed–Muller RM (d, r) code in terms of the Reed–Muller codes RM (d − 1, r) and RM (d − 1, r − 1). The bar...

codes for lossless data compression. Irving S. Reed and David E. Muller proposing Reed–Muller codes in 1954. The 1960 proposal of Reed–Solomon codes....

at P b ( E ) ≈ 10 − 5 {\displaystyle P_{b}(E)\approx 10^{-5}} for Reed–Muller codes of length n ≤ 64 {\displaystyle n\leq 64} : In the bandwidth-limited...

{\displaystyle 2^{m-1}-2^{m/2-1+r}} The code sits between the Kerdock code and the second-order Reed–Muller codes. More precisely, we have K ( m ) ⊆ D G...

code works by including carefully crafted redundancy with the stored (or transmitted) data. Examples include Hamming codes, Reed–Solomon, Reed–Muller...

locally testable codes include Reed-Muller codes (see locally decodable codes for a decoding algorithm), Reed-Solomon codes, and the short code. Gilbert–Varshamov...