Syndrome decoding

In coding theory, decoding is the process of translating received messages into codewords of a given code. There have been many common methods of mapping messages to codewords. These are often used to recover messages sent over a noisy channel, such as a binary symmetric channel.

${\displaystyle C\subset \mathbb {F} _{2}^{n}}$ is considered a binary code with the length ${\displaystyle n}$; ${\displaystyle x,y}$ shall be elements of ${\displaystyle \mathbb {F} _{2}^{n}}$; and ${\displaystyle d(x,y)}$ is the distance between those elements.

...
Wikipedia