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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 ...
A generator matrix for a linear [,,]-code has format , where n is the length of a codeword, k is the number of information bits (the dimension of C as a vector subspace), d is the minimum distance of the code, and q is size of the finite field, that is, the number of symbols in the alphabet (thus, q = 2 indicates a binary code, etc.).
The Hadamard code is a linear code, and all linear codes can be generated by a generator matrix .This is a matrix such that () = holds for all {,}, where the message is viewed as a row vector and the vector-matrix product is understood in the vector space over the finite field.
This LDPC code fragment represents a three-bit message encoded as six bits. Redundancy is used, here, to increase the chance of recovering from channel errors. This is a (6, 3) linear code, with n = 6 and k = 3. Again ignoring lines going out of the picture, the parity-check matrix representing this graph fragment is
C/C++, C#, D, IDL, Fortran, Java, PHP, Python Any 1997/10/26 1.9.1 GPL Epydoc: Edward Loper Text Python Any 2002/01/— 3.0 (2008) MIT: fpdoc (Free Pascal Documentation Generator) Sebastian Guenther and Free Pascal Core Text (Object)Pascal/Delphi FPC tier 1 targets 2005 3.2.2 GPL reusable parts are GPL with static linking exception Haddock ...
Formally, a parity check matrix H of a linear code C is a generator matrix of the dual code, C ⊥. This means that a codeword c is in C if and only if the matrix-vector product Hc ⊤ = 0 (some authors [1] would write this in an equivalent form, cH ⊤ = 0.) The rows of a parity check matrix are the coefficients of the parity check equations. [2]
To do so technically would require a more sophisticated grammar, like a Chomsky Type 1 grammar, also termed a context-sensitive grammar. However, parser generators for context-free grammars often support the ability for user-written code to introduce limited amounts of context-sensitivity. (For example, upon encountering a variable declaration ...
A pseudorandom number generator ( PRNG ), also known as a deterministic random bit generator ( DRBG ), [ 1] is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. The PRNG-generated sequence is not truly random, because it is completely determined by an initial value ...