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  2. Parity bit - Wikipedia

    en.wikipedia.org/wiki/Parity_bit

    Accordingly, there are two variants of parity bits: even parity bit and odd parity bit. In the case of even parity, for a given set of bits, the bits whose value is 1 are counted. If that count is odd, the parity bit value is set to 1, making the total count of occurrences of 1s in the whole set (including the parity bit) an even number.

  3. Parity-check matrix - Wikipedia

    en.wikipedia.org/wiki/Parity-check_matrix

    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]

  4. Hamming (7,4) - Wikipedia

    en.wikipedia.org/wiki/Hamming(7,4)

    The original 4 data bits are converted to seven bits (hence the name "Hamming(7,4)") with three parity bits added to ensure even parity using the above data bit coverages. The first table above shows the mapping between each data and parity bit into its final bit position (1 through 7) but this can also be presented in a Venn diagram .

  5. Project Jupyter - Wikipedia

    en.wikipedia.org/wiki/Project_Jupyter

    A Jupyter Notebook document is a JSON file, following a versioned schema, usually ending with the ".ipynb" extension. The main parts of the Jupyter Notebooks are: Metadata, Notebook format and list of cells. Metadata is a data Dictionary of definitions to set up and display the notebook. Notebook Format is a version number of the software.

  6. Two-out-of-five code - Wikipedia

    en.wikipedia.org/wiki/Two-out-of-five_code

    The requirement that exactly two bits be set is strictly stronger than a parity check; like all constant-weight codes, a two-out-of-five code can detect not only any single-bit error, but any unidirectional error-- cases in which all the individual bit errors are of a single type (all 0→1 or all 1→0).

  7. Parity measurement - Wikipedia

    en.wikipedia.org/wiki/Parity_measurement

    Indirect parity measurements coincide with the typical way we think of parity measurement as described above, by measuring an ancilla qubit to determine the parity of the input bits. Direct parity measurements differ from the previous type in that a common mode with the parities coupled to the qubits is measured, without the need for an ancilla ...

  8. Low-density parity-check code - Wikipedia

    en.wikipedia.org/wiki/Low-density_parity-check_code

    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.

  9. Multidimensional parity-check code - Wikipedia

    en.wikipedia.org/wiki/Multidimensional_parity...

    A multidimensional parity-check code (MDPC) is a type of error-correcting code that generalizes two-dimensional parity checks to higher dimensions. It was developed as an extension of simple parity check methods used in magnetic recording systems and radiation-hardened memory designs .