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A Gray code absolute rotary encoder with 13 tracks. Housing, interrupter disk, and light source are in the top; sensing element and support components are in the bottom. Gray codes are used in linear and rotary position encoders ( absolute encoders and quadrature encoders) in preference to weighted binary encoding.
Traditional Reed–Muller codes are binary codes, which means that messages and codewords are binary strings. When r and m are integers with 0 ≤ r ≤ m, the Reed–Muller code with parameters r and m is denoted as RM ( r , m ). When asked to encode a message consisting of k bits, where holds, the RM ( r , m) code produces a codeword ...
Practical implementations rely heavily on decoding the constituent SPC codes in parallel. LDPC codes were first introduced by Robert G. Gallager in his PhD thesis in 1960, but due to the computational effort in implementing encoder and decoder and the introduction of Reed–Solomon codes, they were mostly ignored until the 1990s.
In computer programming, a magic number is any of the following: A unique value with unexplained meaning or multiple occurrences which could (preferably) be replaced with a named constant. A constant numerical or text value used to identify a file format or protocol (for files, see List of file signatures)
Exponential-Golomb coding generalizes the gamma code to integers with a "flatter" power-law distribution, just as Golomb coding generalizes the unary code. It involves dividing the number by a positive divisor, commonly a power of 2, writing the gamma code for one more than the quotient, and writing out the remainder in an ordinary binary code.
Binary Goppa code. In mathematics and computer science, the binary Goppa code is an error-correcting code that belongs to the class of general Goppa codes originally described by Valerii Denisovich Goppa, but the binary structure gives it several mathematical advantages over non-binary variants, also providing a better fit for common usage in ...
In mathematical terms, Hamming codes are a class of binary linear code. For each integer r ≥ 2 there is a code-word with block length n = 2r − 1 and message length k = 2r − r − 1. Hence the rate of Hamming codes is R = k / n = 1 − r / (2r − 1), which is the highest possible for codes with minimum distance of three (i.e., the minimal ...
One significant application of Reed–Solomon coding was to encode the digital pictures sent back by the Voyager program. Voyager introduced Reed–Solomon coding concatenated with convolutional codes, a practice that has since become very widespread in deep space and satellite (e.g., direct digital broadcasting) communications.