commit 5d349a7d603dc8eb55b2637e5142d59cbaf8acd7
parent 4bd17472ed5dc293204bd7e8593ef99dd441e9cf
Author: Alex Balgavy <alex@balgavy.eu>
Date: Sat, 20 Mar 2021 20:00:50 +0100
Update crypto notes
Diffstat:
1 file changed, 5 insertions(+), 0 deletions(-)
diff --git a/content/coding-and-cryptography/linear-codes/index.md b/content/coding-and-cryptography/linear-codes/index.md
@@ -99,6 +99,11 @@ if G generator matrix for linear code C length n and dimension k, then v = u G r
info rate of (n, k, d) code: $\frac{\log_{2} (2^{k})}{n} = \frac{k}{n}$
+For C is (n,k,d):
+- $\dim C^{\perp} = n - k $
+- $|C| = 2^{k}$
+- $H_{C}$ is n row, n - k cols, rank n - k (nonzero rows in REF)
+
## Parity check matrices
H parity check matrix for linear code C if columns form basis for dual code $C^{\perp}$.
- if C length n dimension k, parity check matrix has n rows, n-k columns, n-k rank
