Check Digit/Examples/Parity Check

Example of Check Digit

An example of a check digit is a parity check:

Let $\LL$ be a linear $\tuple {n, 2}$-code.

Let $\LL'$ be the linear $\tuple {n + 1, 2}$-code formed from $\LL$ by adding an extra bit to the end of each of the codewords of $\LL$ such that the digit sums of each of the codewords of $\LL'$ have the same parity.

This extra bit is the check digit of $\LL'$.


This method of construction of an error-correcting code is called a parity check.


Sources

  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): check digit
  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): check digit (checksum)
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