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  2. Check digit - Wikipedia

    en.wikipedia.org/wiki/Check_digit

    The final digit of a Universal Product Code, International Article Number, Global Location Number or Global Trade Item Number is a check digit computed as follows: [3] [4]. Add the digits in the odd-numbered positions from the left (first, third, fifth, etc.—not including the check digit) together and multiply by three.

  3. Cyclic redundancy check - Wikipedia

    en.wikipedia.org/wiki/Cyclic_redundancy_check

    Since 1993, Koopman, Castagnoli and others have surveyed the space of polynomials between 3 and 64 bits in size, [13] [15] [16] [17] finding examples that have much better performance (in terms of Hamming distance for a given message size) than the polynomials of earlier protocols, and publishing the best of these with the aim of improving the ...

  4. Burst error-correcting code - Wikipedia

    en.wikipedia.org/wiki/Burst_error-correcting_code

    Proof. We need to prove that if you add a burst of length to a codeword (i.e. to a polynomial that is divisible by ()), then the result is not going to be a codeword (i.e. the corresponding polynomial is not divisible by ()).

  5. Checksum - Wikipedia

    en.wikipedia.org/wiki/Checksum

    Check digits and parity bits are special cases of checksums, appropriate for small blocks of data (such as Social Security numbers, bank account numbers, computer words, single bytes, etc.). Some error-correcting codes are based on special checksums which not only detect common errors but also allow the original data to be recovered in certain ...

  6. Error detection and correction - Wikipedia

    en.wikipedia.org/wiki/Error_detection_and_correction

    A checksum of a message is a modular arithmetic sum of message code words of a fixed word length (e.g., byte values). The sum may be negated by means of a ones'-complement operation prior to transmission to detect unintentional all-zero messages.

  7. Hamming (7,4) - Wikipedia

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

    This table describes which parity bits cover which transmitted bits in the encoded word. For example, p 2 provides an even parity for bits 2, 3, 6, and 7. It also details which transmitted bit is covered by which parity bit by reading the column.

  8. Mathematics of cyclic redundancy checks - Wikipedia

    en.wikipedia.org/wiki/Mathematics_of_cyclic...

    CRCs are convenient and popular because they have good error-detection properties and such a multiple may be easily constructed from any message polynomial by appending an -bit remainder polynomial to produce () = + (), where is the degree of the generator polynomial.

  9. Verhoeff algorithm - Wikipedia

    en.wikipedia.org/wiki/Verhoeff_algorithm

    The analysis broke the errors down into a number of categories: first, by how many digits are in error; for those with two digits in error, there are transpositions (ab → ba), twins (aa → 'bb'), jump transpositions (abc → cba), phonetic (1a → a0), and jump twins (aba → cbc). Additionally there are omitted and added digits.