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The generator matrix The Reed–Muller RM (r, m) code of order r and length N = 2 m is the code generated by v0 and the wedge products of up to r of the vi, 1 ≤ i ≤ m (where by convention a wedge product of fewer than one vector is the identity for the operation).
Generator matrix In coding theory, a generator matrix is a matrix whose rows form a basis for a linear code. The codewords are all of the linear combinations of the rows of this matrix, that is, the linear code is the row space of its generator matrix.
Roblox ( / ˈroʊblɒks / ROH-bloks) is an online game platform and game creation system developed by Roblox Corporation that allows users to program and play games created by themselves or other users. Created by David Baszucki and Erik Cassel in 2004 and released in 2006, the platform hosts user-created games of multiple genres coded in the programming language Lua. For most of Roblox ' s ...
Parity-check matrix In coding theory, a parity-check matrix of a linear block code C is a matrix which describes the linear relations that the components of a codeword must satisfy. It can be used to decide whether a particular vector is a codeword and is also used in decoding algorithms.
LDPC codes have been shown to have ideal combinatorial properties. In his dissertation, Gallager showed that LDPC codes achieve the Gilbert–Varshamov bound for linear codes over binary fields with high probability. In 2020 it was shown that Gallager's LDPC codes achieve list decoding capacity and also achieve the Gilbert–Varshamov bound for linear codes over general fields. [9]
Linear code In coding theory, a linear code is an error-correcting code for which any linear combination of codewords is also a codeword. Linear codes are traditionally partitioned into block codes and convolutional codes, although turbo codes can be seen as a hybrid of these two types. [1] Linear codes allow for more efficient encoding and decoding algorithms than other codes (cf. syndrome ...
The parity-check matrix of a Hamming code is constructed by listing all columns of length r that are non-zero, which means that the dual code of the Hamming code is the shortened Hadamard code, also known as a Simplex code. The parity-check matrix has the property that any two columns are pairwise linearly independent .
The daughter of the late Nobel laureate Alice Munro has accused the author's second husband, Gerard Fremlin, of sexual abuse, writing that her mother remained with him because she “loved him too ...