<jupyter_start><jupyter_text>Parity check matricesIn LDPC error correction codes are represented in terms of their parity check matrix stored in `numpy.ndarray` format. As an example, the parity check matrix for the repetition code can be loaded from the `ldpc.codes` submodule as follows:<jupyter_code>import numpy as np
from ldpc.codes import rep_code
n=5 #specifies the lenght of the repetition code
H=rep_code(n) #returns the repetition code parity check matrix
print(H)<jupyter_output>[[1 1 0 0 0]
 [0 1 1 0 0]
 [0 0 1 1 0]
 [0 0 0 1 1]]<jupyter_text>To compute the [n,k,d] code parameters we can use functions from the `ldpc.mod2` and `ldpc.code_util` submodules. Below is an example showing how to calculate the code parameters of the Hamming code:<jupyter_code>from ldpc.codes import hamming_code #function for generating Hamming codes
from ldpc.mod2 import rank #function for calcuting the mod2 rank
from ldpc.code_util import compute_code_distance #function for calculting the code distance

H=hamming_code(3)
print(H)
n=H.shape[1] #block length of the code
k=n-rank(H) #the dimension of the code computed using the rank-nullity theorem.
d=compute_code_distance(H) #computes the code distance
print(f"Hamming code parameters: [n={n},k={k},d={d}]")<jupyter_output>[[0 0 0 1 1 1 1]
 [0 1 1 0 0 1 1]
 [1 0 1 0 1 0 1]]
Hamming code parameters: [n=7,k=4,d=3]
StarcoderdataJupyterStructuredCleanDedup