Definition:Dual Code

Definition

Let $C$ be a binary linear code of length $n$.

The dual code to $C$ is the set of all binary strings $b_1 b_2 \cdots b_n$ such that:

$a_1 b_1 + a_2 b_2 + \cdots + a_n b_n = 0 \pmod 2$

for all codewords $a_1 a_2 \cdots a_n$ in $C$.

Also see

• Results about dual codes can be found here.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): dual code