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The two-dimensional parity-check code, usually called the optimal rectangular code, is the most popular form of multidimensional parity-check code. Assume that the goal is to transmit the four-digit message "1234", using a two-dimensional parity scheme. First the digits of the message are arranged in a rectangular pattern: 12 34
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 [1] would write this in an equivalent form, cH ⊤ = 0.) The rows of a parity check matrix are the coefficients of the parity check equations. [2]
For general , the generator matrix of the augmented Hadamard code is a parity-check matrix for the extended Hamming code of length and dimension , which makes the augmented Hadamard code the dual code of the extended Hamming code. Hence an alternative way to define the Hadamard code is in terms of its parity-check matrix: the parity-check ...
A qubit is a two-level system, and when we measure one qubit, we can have either 1 or 0 as a result. One corresponds to odd parity, and zero corresponds to even parity. This is what a parity check is. This idea can be generalized beyond single qubits. This can be generalized beyond a single qubit and it is useful in QEC.
While the terms allude to the rows and columns of a two-dimensional array, i.e. a matrix, the orders can be generalized to arrays of any dimension by noting that the terms row-major and column-major are equivalent to lexicographic and colexicographic orders, respectively. It is also worth noting that matrices, being commonly represented as ...
W3Schools is a freemium educational website for learning coding online. [1] [2] Initially released in 1998, it derives its name from the World Wide Web but is not affiliated with the W3 Consortium. [3] [4] [unreliable source] W3Schools offers courses covering many aspects of web development. [5] W3Schools also publishes free HTML templates.
Database normalization is the process of structuring a relational database accordance with a series of so-called normal forms in order to reduce data redundancy and improve data integrity.
The parity bit may be used within another constituent code. In an example using the DVB-S2 rate 2/3 code the encoded block size is 64800 symbols (N=64800) with 43200 data bits (K=43200) and 21600 parity bits (M=21600). Each constituent code (check node) encodes 16 data bits except for the first parity bit which encodes 8 data bits.