The Hadamard code is an error-correcting code named after the French mathematician Jacques Hadamard that is used for error detection and correction when...

of Hadamard's maximal determinant problem. Certain Hadamard matrices can almost directly be used as an error-correcting code using a Hadamard code (generalized...

Hadamard code is a [ 2 r , r , 2 r − 1 ] 2 {\displaystyle [2^{r},r,2^{r-1}]_{2}} linear code and is capable of correcting many errors. Hadamard code could...

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...

practical interest Goppa code, used in the McEliece cryptosystem Hadamard code Hagelbarger code Hamming code Latin square based code for non-white noise (prevalent...

computational mathematics, the Hadamard ordered fast Walsh–Hadamard transform (FWHTh) is an efficient algorithm to compute the Walsh–Hadamard transform (WHT). A naive...

science. Reed–Muller codes generalize the Reed–Solomon codes and the Walsh–Hadamard code. Reed–Muller codes are linear block codes that are locally testable...

The Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is...

codes, Hadamard codes, Expander codes, Golay codes, Reed–Muller codes and Polar codes. These examples also belong to the class of linear codes, and hence...

Instead of using a repetition code, a [32, 6, 16] Hadamard code was used, which is also a 1st-order Reed-Muller code. Errors of up to seven bits per...

by only one. Gold codes are used in GPS. The GPS C/A ranging codes are Gold codes of period 1,023. Hadamard code JPL code Kasami code Zadoff–Chu sequence...

most famous error-correcting codes, the Hadamard code, is a locally testable code. A codeword x is encoded in the Hadamard code to be the linear function...

Locally decodable codes are especially useful for data transmission over noisy channels. The Hadamard code (a special case of Reed Muller codes) was used in...

code K {\displaystyle {\mathit {K}}} form a Hadamard exponent. Thus, x K {\displaystyle {\mathit {xK}}} is the standard form of some complex Hadamard...

In coding theory, concatenated codes form a class of error-correcting codes that are derived by combining an inner code and an outer code. They were conceived...

sometimes included in instruction sets. The Hadamard or Walsh-Hadamard gate, named after Jacques Hadamard (French: [adamaʁ]) and Joseph L. Walsh, acts...

Reed–Muller, Walsh–Hadamard, Bose–Chaudhuri–Hochquenghem, Turbo, Golay, algebraic geometry codes, low-density parity-check codes, and space–time codes. Error detecting...

uses of balanced-weight codes include biphase mark code uses a 1 of 2 code; 6b/8b encoding uses a 4 of 8 code; the Hadamard code is a 2 k − 1 {\displaystyle...

Hadamard may refer to: Zélie Hadamard (1849–1901), French actress Jacques Hadamard (1865–1963), a French mathematician, whose name is associated with the...

function Hadamard code Hadamard's dynamical system Hadamard manifold Hadamard matrix Hadamard space Hadamard Transform and Hadamard gate Hadamard variance...

gate with respect to a Hadamard transformed basis { | + ⟩ , | − ⟩ } {\displaystyle \{|+\rangle ,|-\rangle \}} . The Hadamard transformed basis of a one-qubit...

This is a list of algebraic coding theory topics....

Voyager probes, as it is much more compact than the previously-used Hadamard code. Quantizers, or analog-to-digital converters, can use lattices to minimise...

= 2 2 k {\displaystyle 2^{n}=2^{2^{k}}} . The Walsh-Hadamard code is a subcode of the long code, and can be obtained by only using functions f i {\displaystyle...

one-way functions can be viewed as an algorithm for list-decoding the Hadamard code). Goldwasser, S. and Bellare, M. "Lecture Notes on Cryptography" Archived...

In mathematics, the Paley construction is a method for constructing Hadamard matrices using finite fields. The construction was described in 1933 by the...

transmissions. Zadoff–Chu sequences are an improvement over the Walsh–Hadamard codes used in UMTS because they result in a constant-amplitude output signal...

derived from the ordering of the Hadamard matrix by first applying the bit-reversal permutation and then the Gray-code permutation: W ( 8 ) = [ 1 1 1 1...

phase flip. Then the bit-flip code from above can recover | ψ ⟩ {\displaystyle |\psi \rangle } by transforming into the Hadamard basis before and after transmission...

in quantum algorithms such as: Controlled-not with many target qubits, Hadamard operation on many qubits, Phase and controlled phase. Quantum algorithms...