Coding Theory Calculator

Coding Theory Calculator

Syndrome Decoding

Definition - Syndrome

Let $H$ be a PCM for an $(n,k)$ -code $C$ over $F$ . Let $x \in V_n(F)$ . The syndrome of $x$ (w.r.t. $H$ ) is $s = Hx^T$ .

Algorithm - Syndrome Decoding Algorithm (CMLD) for General Binary Linear Codes

Input: PCM $H$ and a received word $r \in V_n(F)$ .

1:
Create a table of coset leaders and their syndromes.
2:
Compute $s = Hr^T$
3:
Look up the coset leader corresponding to $s$ , say $\ell$ .
4:
Decode $r$ to $c = r - \ell$ .

Decoded Word

PCM H

Rows

2

Columns

2

Received Word r