Parity Check/Examples/Arbitrary Example 1

Example of Parity Check

Consider the linear $\tuple {2, 2}$-code:

$\set {00, 01, 10, 11}$

Adding a check bit for a parity check, the new codewords become:

$\set {000, 011, 101, 110}$

to ensure the number of $1$s is even.


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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