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,...

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...

is in terms of its parity-check matrix: the parity-check matrix of the Hadamard code is equal to the generator matrix of the Hamming code. Hadamard codes...

row of a systematic generator matrix whose non-identity part takes k = 32771 bits. The private key, a quasi-cyclic parity-check matrix with d = 274 nonzero...

decoding algorithm. The generator matrix for the Barnes-Wall Lattice B W 16 {\displaystyle BW_{16}} is given by the following matrix: M B W 16 = 1 2 ( 1 1...

process infinitesimal generator matrix, of a continuous time Markov chain, a class of stochastic processes Infinitesimal generator of a strongly continuous...

related to DataMatrix. GS1 DataMatrix Guideline: Overview and technical introduction to the use of GS1 DataMatrix Datamatrix Code Generator - Online Tool...

^{m}} . Thus the block length is n = q m {\displaystyle n=q^{m}} . A generator matrix for a Reed–Muller code RM(r, m) of length N = 2m can be constructed...

probability theory, a transition-rate matrix (also known as a Q-matrix, intensity matrix, or infinitesimal generator matrix) is an array of numbers describing...

win. 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...

on the left hand side of G. The code generator matrix G {\displaystyle \mathbf {G} } and the parity-check matrix H {\displaystyle \mathbf {H} } are: G...

disguising the selected code as a general linear code. For this, the code's generator matrix G {\displaystyle G} is perturbated by two randomly selected invertible...

{\displaystyle \dim C+\dim C^{\perp }=n.} A generator matrix for the dual code is the parity-check matrix for the original code and vice versa. The dual...

capable of extracting water from air Generator (mathematics) Generator matrix, a matrix used in coding theory Generator (category theory) of a category, in...

the parity check matrix is n − k {\displaystyle n-k} . Another simple proof follows from observing that the rows of any generator matrix in standard form...

Vigilant. She, Vector, and Soren attack a backup power generator for the local power plant in the Matrix to assist Neo in reaching the Source, but are all...

pseudocode shows how to generate a reduced generator matrix: function function_name is // Initialize G with identity matrix augmented with ones column G ← [I_{r1-1}...

error. Example : The linear block code with the following generator matrix and parity check matrix is a [ 7 , 4 , 3 ] 2 {\displaystyle [7,4,3]_{2}} Hamming...

Prange: Let G {\displaystyle G} be the k × n {\displaystyle k\times n} generator matrix of C {\displaystyle C} used for encoding. Select k {\displaystyle k}...

span of the columns of its generator matrix, a 24×24 matrix with determinant 1. Leech generator matrix A 24x24 generator (in row convention) for the...

representation of the infinitesimal generators of the special unitary group SU(3). Hamiltonian matrix — a matrix used in a variety of fields, including...

check matrix for this generator matrix is [ − B | I 6 ] T {\displaystyle [-B|I_{6}]^{T}} , where T {\displaystyle T} denotes the transpose of the matrix. An...

rotation matrix or differential rotation matrix is a matrix representing an infinitely small rotation. While a rotation matrix is an orthogonal matrix R T...

codes, two Hamming matrices can be defined: the code generator matrix G and the parity-check matrix H: G T := ( 1 1 0 1 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0 0...

In mathematics, the term Cartan matrix has three meanings. All of these are named after the French mathematician Élie Cartan. Amusingly, the Cartan matrices...

code is a linear code, and in the classical encoding procedure, its generator matrix is A {\displaystyle A} . There are alternative encoding procedures...

and 3 are swapped. Step 4: Row 1 is added to row 3. From this, the generator matrix G can be obtained as [ I k | P ] {\displaystyle...

where A ( t ) {\displaystyle A(t)} is the transition rate matrix (also known as the generator matrix), while the Kolmogorov backward equations are ∂ P i j...

is defined by its generator matrix, which we choose to be a random k × n {\displaystyle k\times n} generator matrix; that is, a matrix of k n {\displaystyle...

distance of the code is larger. For a systematic linear code, the generator matrix, G {\displaystyle G} , can always be written as G = [ I k | P ] {\displaystyle...