Search results
Results From The WOW.Com Content Network
The generator matrix. The Reed–Muller RM(r, m) code of order r and length N = 2 m is the code generated by v 0 and the wedge products of up to r of the v i, 1 ≤ i ≤ m (where by convention a wedge product of fewer than one vector is the identity for the
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.).
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 ...
LDPC codes functionally are defined by a sparse parity-check matrix. This sparse matrix is often randomly generated, subject to the sparsity constraints—LDPC code construction is discussed later. These codes were first designed by Robert Gallager in 1960. Below is a graph fragment of an example LDPC code using Forney's factor graph notation.
A generator matrix for the binary Golay code is I A, where I is the 12×12 identity matrix, and A is the complement of the adjacency matrix of the icosahedron. A convenient representation. It is convenient to use the "Miracle Octad Generator" format, with co-ordinates in an array of 4 rows, 6 columns. Addition is taking the symmetric difference.
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 would write this in an equivalent form, cH ⊤ = 0.) The rows of a parity check matrix are the coefficients of the parity check equations.
Hamming (7,4) In coding theory, Hamming (7,4) is a linear error-correcting code that encodes four bits of data into seven bits by adding three parity bits. It is a member of a larger family of Hamming codes, but the term Hamming code often refers to this specific code that Richard W. Hamming introduced in 1950.
Sphinx converts reStructuredText files into HTML websites and other formats including PDF, EPub, Texinfo and man. reStructuredText is extensible, and Sphinx exploits its extensible nature through a number of extensions – for autogenerating documentation from source code, writing mathematical notation or highlighting source code, etc. HTML themes