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Matrix generating a linear code
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,
Generator_matrix
Part of coding theory
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
Parity-check_matrix
Matrix describing continuous-time Markov chains
probability theory, a transition-rate matrix (also known as a Q-matrix, intensity matrix, or infinitesimal generator matrix) is an array of numbers describing
Transition-rate_matrix
Error-correcting code
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
Hadamard_code
Two-dimensional matrix barcode
related to DataMatrix. GS1 DataMatrix Guideline: Overview and technical introduction to the use of GS1 DataMatrix Datamatrix Code Generator - Online Tool
Data_Matrix
Type of linear error-correcting code
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
Binary_Golay_code
Family of linear error-correcting codes
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
Hamming_code
Error-correcting codes used in wireless communication
^{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
Reed–Muller_code
Cryptography secured against quantum computers
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
Post-quantum_cryptography
Asymmetric encryption algorithm developed by Robert McEliece
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
McEliece_cryptosystem
Topics referred to by the same term
capable of extracting water from air Generator (mathematics) Generator matrix, a matrix used in coding theory Generator (category theory) of a category, in
Generator
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
Barnes–Wall_lattice
{\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
Dual_code
Pair of related error-correcting codes
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
Ternary_Golay_code
Upper bound in coding theory
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
Singleton_bound
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
List of Matrix series characters
List_of_Matrix_series_characters
Topics referred to by the same term
process infinitesimal generator matrix, of a continuous time Markov chain, a class of stochastic processes Infinitesimal generator of a strongly continuous
Infinitesimal_generator
Class of error-correcting code
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
Linear_code
24-dimensional repeating pattern of points
span of the columns of its generator matrix, a 24×24 matrix with determinant 1. Leech generator matrix A 24×24 generator (in row convention) for the
Leech_lattice
Error-correcting codes
code is a linear code, and in the classical encoding procedure, its generator matrix is A {\displaystyle A} . There are alternative encoding procedures
Reed–Solomon_error_correction
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}
Multidimensional parity-check code
Multidimensional_parity-check_code
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
Gilbert–Varshamov bound for linear codes
Gilbert–Varshamov_bound_for_linear_codes
Linear error-correcting code
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
Hamming(7,4)
Equations characterizing continuous-time Markov processes
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
Kolmogorov_equations
representation of the infinitesimal generators of the special unitary group SU(3). Hamiltonian matrix — a matrix used in a variety of fields, including
List_of_named_matrices
Barcode ScannerSetting Manual" (PDF). sparkfun.com. Datalogic 2 of 5 description Matrix 2 of 5 and Datalogic 2 of 5 generator Matrix 2 of 5 structure
Matrix_2_of_5
Linear error correcting code
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
Low-density_parity-check_code
Algorithms to decode messages
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}
Decoding_methods
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
Systematic_code
Examples of the probabilistic construct
has been working since its last repair. The transition rate matrix (or generator matrix) Q {\displaystyle Q} for this system is: Q = ( − λ λ μ − μ )
Examples_of_Markov_chains
Family of linear transformations
operations of ordinary matrix addition and multiplication of a matrix by a number, forms a vector space over the real numbers. The generators Jx, Jy, Jz, Kx,
Lorentz_transformation
Stochastic differential equation
mathematics — specifically, in stochastic analysis — the infinitesimal generator of a Feller process (i.e. a continuous-time Markov process satisfying
Infinitesimal generator (stochastic processes)
Infinitesimal_generator_(stochastic_processes)
Pseudorandom number generator
The Mersenne Twister is a general-purpose pseudorandom number generator (PRNG) developed in 1997 by Makoto Matsumoto (松本 眞) and Takuji Nishimura (西村 拓士)
Mersenne_Twister
Algorithm for generating pseudo-randomized numbers
A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear
Linear_congruential_generator
of symbols from the code's alphabet. For example, considering the generator matrix G = ( ( 00 11 ) ( 01 01 ) ( 11 01 ) ( 00 11 ) ( 11 11 ) ( 00 00 ) )
Group_code
Random number generators are important in many kinds of technical applications, including physics, engineering or mathematical computer studies (e.g.,
List of random number generators
List_of_random_number_generators
Problem in information theory and communication
{\displaystyle 3} . Given the generator matrix G {\displaystyle \mathbf {G} } of the original Hamming code, the generator matrix G 1 {\displaystyle \mathbf
Distributed_source_coding
Type of matrix
rotation matrix or differential rotation matrix is a matrix representing an infinitely small rotation. While a rotation matrix is an orthogonal matrix R T
Infinitesimal_rotation_matrix
Mathematical model in queueing theory
arrival process has generator matrix, Q = [ S S 0 α 0 0 … 0 S S 0 α 0 … 0 0 S S 0 α … ⋮ ⋮ ⋱ ⋱ ⋱ ] {\displaystyle Q=\left[{\begin{matrix}S&{\boldsymbol {S}}^{0}{\boldsymbol
Markovian_arrival_process
Square matrix whose off-diagonal entries are nonnegative
property for the exponential of a nonnegative matrix. This is natural, once one observes that the generator matrices of continuous-time Markov chains are
Metzler_matrix
Matrices named after Élie Cartan
In mathematics, the term Cartan matrix has three meanings. All of these are named after the French mathematician Élie Cartan. Amusingly, the Cartan matrices
Cartan_matrix
Random process independent of past history
identity matrix of size n, and 0n,n is the zero matrix of size n×n. Multiplying together stochastic matrices always yields another stochastic matrix, so Q
Markov_chain
Computer printing process
serial impact dot matrix printer (SIDM), the OKI Wiredot. The printer supported a character generator for 128 characters with a print matrix of 7 × 5. It was
Dot_matrix_printing
Discrete device in an electronic system
Electrical generator – an electromechanical power source Piezoelectric generator - generates electricity from mechanical strain Van de Graaff generator - generates
Electronic_component
processes "Meta-generator" CompHEP – automatic evaluation of tree level matrix elements for event generation or export into other event generators M. L. Mangano
Event_generator
Matrix operation generalizing exponentiation of scalar numbers
In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems
Matrix_exponential
Pictorial representation of symmetry
symmetric matrix M which has 1s on its diagonal. (Thus each generator r i {\displaystyle r_{i}} has order 2.) This matrix M, the Coxeter matrix, completely
Coxeter–Dynkin_diagram
Class of error correction codes
RA codes. IRA replaces the outer code in RA code with a low density generator matrix code. IRA codes first repeats information bits different times, and
Repeat-accumulate_code
Matrices important in quantum mechanics and the study of spin
delta. I denotes the 2 × 2 identity matrix. These anti-commutation relations make the Pauli matrices the generators of a representation of the Clifford
Pauli_matrices
Electrical generator that uses heat from radioactive decay
A radioisotope thermoelectric generator (RTG, RITEG), or radioisotope power system (RPS), is a type of nuclear battery that uses an array of thermocouples
Radioisotope thermoelectric generator
Radioisotope_thermoelectric_generator
Formulation of quantum mechanics
the infinitesimal generator of the canonical transformation. In quantum mechanics, the quantum analog G is now a Hermitian matrix, and the equations
Matrix_mechanics
Group that admits a formal description in terms of reflections
modified, being proportional to the dot product of the pairwise generators. The Schläfli matrix is useful because its eigenvalues determine whether the Coxeter
Coxeter_group
easily shown based on the idea of defining a generator matrix for the concatenated code in terms of the generator matrices of Cout and Cin. A natural concept
Concatenated error correction code
Concatenated_error_correction_code
{\displaystyle 8679.2} for the matrix size N = 240 {\displaystyle N=240} . That generator occupies less than 2 kb, and if a smaller generator state is required, a
MIXMAX_generator
Mathematical operation on invertible matrices
mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus a generalization
Logarithm_of_a_matrix
Mathematical concept
In mathematics, a symplectic matrix is a 2 n × 2 n {\displaystyle 2n\times 2n} matrix M {\displaystyle M} with real entries that satisfies the condition
Symplectic_matrix
Procedure in quantum information science
matrix for a quantum circuit can also be constructed using these principles. For some message x encoded as Gx, where G corresponds to the generator matrix
Parity_measurement
_{i=0}^{k-1}\left\lceil {\frac {d}{2^{i}}}\right\rceil .} Let G be a generator matrix of C. We can always suppose that the first row of G is of the form
Griesmer_bound
between states 1 and 2 according to a continuous time Markov chain with generator matrix Q = ( − α α β − β ) . {\displaystyle Q={\begin{pmatrix}-\alpha &\alpha
Fluid_queue
Matrix representing the effect of scattering on a physical system
In physics, the S-matrix or scattering matrix is a matrix that relates the initial state and the final state of a physical system undergoing a scattering
S-matrix
This is a list of notable lexer generators and parser generators for various language classes. Regular languages are a category of languages (sometimes
Comparison of parser generators
Comparison_of_parser_generators
Coding Theory
vector c {\displaystyle c} by multiplying m {\displaystyle m} by the generator matrix G = ( 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 32 32 32 32 32 38 38
Locally_recoverable_code
Matrix with nonzero elements on the main diagonal and the diagonals above and below it
matrix can be written as a single-pair matrix (a.k.a. generator-representable semiseparable matrix) of the form ( α 1 − β 1 − β 1 α 2 − β 2 ⋱ ⋱ ⋱ ⋱ ⋱ −
Tridiagonal_matrix
Synthesizer composed of separate modules
voltage-controlled filters, voltage-controlled amplifiers and envelope generators. A modular synth is made up of individual modules which are combined into
Modular_synthesizer
Generative adversarial network variant
provides a better learning signal to the generator. This allows the training to be more stable when generator is learning distributions in very high dimensional
Wasserstein_GAN
Device to generate electricity from wind
forerunner of modern horizontal-axis wind generators was in service at Yalta, USSR, in 1931. This was a 100 kW generator on a 30-meter (98 ft) tower. It was
Wind_turbine
Widely used NTSC television test pattern
LB-819 on February 7, 1951. U.S. patent 2,742,525 Color Test Pattern Generator (since expired) was awarded on April 17, 1956, to Larky and Holmes. Later
SMPTE_color_bars
Motor vehicle platform
German to "Modular Longitudinal Matrix". MLB is one strategy within VW's overall MB (Modulare Baukasten or modular matrix) program which also includes the
Volkswagen_Group_MLB_platform
Modular monophonic analog synthesizer
musical instruments ever made." It is notable for being programmed via matrix switches instead of conventional patch cables. Demand for smaller and more
ARP_2500
figure. The circuit model using dependent generators is just an alternative way of representing this matrix. Chitode, J.S. Communication Theory. Technical
Generator_(circuit_theory)
Analogue synthesizer
keyboardless, six-voice version of the Matrix-12 (released a year later, in 1985). Utilizing Oberheim's Matrix Modulation technology, the Xpander combined
Oberheim_Xpander
248-dimensional exceptional simple Lie group
Cartan matrix of a rank r root system is an r × r matrix whose entries are derived from the simple roots. Specifically, the entries of the Cartan matrix are
E8_(mathematics)
Social network game played on a two-dimensional matrix
stories. Images of the Poietic Generator Illustration of the concept (1988) Each player draws on one element of the total matrix Interface, Multicast version
Poietic_Generator
{\displaystyle C} is a linear code, its generator matrix is an ( n × s ) {\displaystyle (n\times s)} -matrix A {\displaystyle A} over F 2 {\displaystyle
Small-bias_sample_space
Mathematical function often applied to matrices
norm. It quantifies key notions such as positive/negative definiteness in matrix theory, uniformly coercive or monotone vector fields in nonlinear analysis
Logarithmic_norm
Determining all voltages and currents within an electrical network
voltage generator into a current generator using Norton's theorem in order to be able to later combine the internal resistance of the generator with a
Network analysis (electrical circuits)
Network_analysis_(electrical_circuits)
Error-correcting code
to the complexity of constructing its generator matrix G. That in effect means that we can compute the matrix in logarithmic space without using the
Justesen_code
Movement with a fixed point is rotation
Aθ is the "generator" of the particular rotation, being the vector (x,y,z) associated with the matrix A. This shows that the rotation matrix and the axis–angle
Euler's_rotation_theorem
Statistical measure of how far values spread from their average
consider that a theoretical probability distribution can be used as a generator of hypothetical observations. If an infinite number of observations are
Variance
Algorithm for shuffling a finite sequence
random number generator used. An additional problem occurs when the Fisher–Yates shuffle is used with a pseudorandom number generator or PRNG: as the
Fisher–Yates_shuffle
Form of a matrix indicating its eigenvalues and their algebraic multiplicities
_{n}{\color {red}\lrcorner }\\\end{array}}\right]} Example of a matrix in Jordan normal form. All matrix entries not shown are zero. The outlined squares are known
Jordan_normal_form
Families of matrices in mathematics, physics, and quantum information
traditional Pauli matrices are the matrix representation of the s u ( 2 ) {\displaystyle {\mathfrak {su}}(2)} Lie algebra generators J x {\displaystyle J_{x}}
Generalizations of Pauli matrices
Generalizations_of_Pauli_matrices
Class of pseudorandom number generators
return x * 0x2545F4914F6CDD1DULL; } The generator fails only the MatrixRank test of BigCrush, however if the generator is modified to return only the high
Xorshift
Orientable surface whose boundary is a knot or link
transpose matrix. Every integer 2g × 2g matrix V {\displaystyle V} with V − V ∗ = Q {\displaystyle V-V^{*}=Q} arises as the Seifert matrix of a knot with
Seifert_surface
Collaborative pixel art website
the contested Santa Rosa island. Poietic Generator – Social network game played on a two-dimensional matrix r/place – Online social experiment on Reddit
Wplace
Japanese sports car / grand tourer
carbon fibre reinforced plastic (CFRP). The transaxle integrates a motor–generator, a newly developed rear-mounted eight-speed automatic transmission using
Toyota_GR_GT
Barcode format
algorithm with a font-based barcode solution. Online barcode generator – Free online Barcode generator for the various barcode types. Python Bar Code 128 – Python
Code_128
Type of group and algebra representation
Brauer from the 1940s to give modular representation theory, in which the matrix operators act on a vector space over a field K {\displaystyle K} of arbitrary
Irreducible_representation
Irreducible representation of the rotation group SO
The Wigner D-matrix is a unitary matrix in an irreducible representation of the groups SU(2) and SO(3). It was introduced in 1927 by Eugene Wigner, and
Wigner_D-matrix
Algebraic structure used in analysis
{\displaystyle G} may be called a set of generators for G {\displaystyle G} . (They are "infinitesimal generators" for G {\displaystyle G} , so to speak
Lie_algebra
Type of matrix barcode
The Aztec Code is a matrix code invented by Andrew Longacre, Jr. and Robert Hussey in 1995. The code was published by AIM, Inc. in 1997. Although the Aztec
Aztec_Code
Generalization of gamma distribution to multiple dimensions
Multivariate Analysis". J. Amer. Statist. Assoc. 62 (318): 607–625. doi:10.1080/01621459.1967.10482934. JSTOR 2283988. A C++ library for random matrix generator
Wishart_distribution
Classification system for symmetry groups in geometry
reflections φ0,1,2 (and matrix V0,1,2), like the index 4 subgroup : [4+,4+] = . Another composite generator, by convention as ζ (and matrix Z), represents the
Coxeter_notation
Full-size luxury SUV
152 PS) 1.5-liter turbocharged port-injected gasoline engine acting as a generator. The all-wheel drive layout is powered by two electric motors producing
AITO_M9
Type of mathematical group
In mathematics, a matrix group is a group G consisting of invertible matrices over a specified field K, with the operation of matrix multiplication. A
Linear_group
Collection of masculist and misogynistic websites and forums
described as "taking the red pill", a metaphor borrowed from the film The Matrix. The manosphere overlaps with the far-right and alt-right communities. It
Manosphere
Group that is also a differentiable manifold with group operations that are smooth
modern mathematics and physics. Lie groups were first found by studying matrix subgroups G {\displaystyle G} contained in GL n ( R ) {\displaystyle
Lie_group
Theorem in theoretical physics
the S-matrix. Supergravity S-matrix Haag, R.; Łopuszański, J.T.; Sohnius, M. (1975). "All possible generators of supersymmetries of the S-matrix". Nuclear
Haag–Łopuszański–Sohnius theorem
Haag–Łopuszański–Sohnius_theorem
Graphical language for quantum processes
string diagrams called ZX-diagrams. A ZX-diagram consists of a set of generators called spiders that represent specific tensors. These are connected together
ZX-calculus
Numerical analysis of electric power flow
any generators connected to it is called a Load Bus. With one exception, a bus with at least one generator connected to it is called a Generator Bus.
Power-flow_study
GENERATOR MATRIX
GENERATOR MATRIX
Boy/Male
Tamil
Young generation
Girl/Female
Indian, Tamil
Generation
Boy/Male
Biblical
Nativity, generation.
Girl/Female
Biblical
Nativity, generation.
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Punjabi
Generation; Coming Generation of Father; Family
Boy/Male
Muslim
Old generation
Boy/Male
Indian, Punjabi, Sikh
New Generation
Boy/Male
Indian
Young Generation
Girl/Female
Biblical
A generation.
Boy/Male
Hindu, Indian
Young Generation
Boy/Male
Biblical, British, English
Nativity; Generation
Boy/Male
Gujarati, Hindu, Indian, Kannada
Era; Generation
Boy/Male
Indian, Telugu
Generated
Boy/Male
Biblical
Nativity, generation.
Boy/Male
Tamil
Forthcoming generation
Girl/Female
Biblical
Generation, habitation.
Boy/Male
British, Czech, Hindu, Indian
New Generation
Boy/Male
Japanese Welsh
Large; generation.
Girl/Female
Indian
Generation
Girl/Female
Biblical
Birth, generation.
GENERATOR MATRIX
GENERATOR MATRIX
Boy/Male
Czechoslovakian
First.
Girl/Female
English
Form of the Greek Catherine meaning pure.
Surname or Lastname
English
English : from a Biblical personal name, meaning in Hebrew ‘God is (my) light’, which was popular among the Puritans, especially among early settlers in New England, but also in the southern states. In the First and Second Books of Samuel, Abner is Saul’s uncle and the commander of his army, who is eventually cut down by Joab (II Samuel 3:12–39).
Surname or Lastname
English
English : variant of Keighley.
Girl/Female
Arabic
Daughter; Girl
Boy/Male
Indian, Malayalam
God Shiva
Girl/Female
Hindu, Indian
Queen
Female
Hebrew
(× Ö´×¡Ö¸×”) Variant spelling of Hebrew Nisa, NISSA means "to test."
Boy/Male
Hindu
Lord Shiva, Conqueror of death
Girl/Female
Hindu, Indian, Tamil
Full Moon
GENERATOR MATRIX
GENERATOR MATRIX
GENERATOR MATRIX
GENERATOR MATRIX
GENERATOR MATRIX
n.
That which is generated or brought forth; progeny; offspiring.
v. t.
To beget; to procreate; to propagate; to produce (a being similar to the parent); to engender; as, every animal generates its own species.
n.
Same as Regenerator.
n.
Generation by means of ova. See Generation.
n.
Spontaneous generation.
n.
An apparatus in which vapor or gas is formed from a liquid or solid by means of heat or chemical process, as a steam boiler, gas retort, or vessel for generating carbonic acid gas, etc.
n.
One who, or that which, generates, begets, causes, or produces.
p. pr. & vb. n.
of Generate
v. i.
Generation.
n.
Same as Generation.
n.
The principal sound or sounds by which others are produced; the fundamental note or root of the common chord; -- called also generating tone.
n.
The formation or production of any geometrical magnitude, as a line, a surface, a solid, by the motion, in accordance with a mathematical law, of a point or a magnitude; as, the generation of a line or curve by the motion of a point, of a surface by a line, a sphere by a semicircle, etc.
n.
One who venerates.
imp. & p. p.
of Generate
n.
One who begets; a generator; an originator.
n.
Origination by some process, mathematical, chemical, or vital; production; formation; as, the generation of sounds, of gases, of curves, etc.
a.
Generated by water.
n.
Race; generation; birth.
n.
Generation; procreation; birth.
n.
Alternate generation. See under Generation.