diff --git a/python_test/test_simplex_code.py b/python_test/test_simplex_code.py
new file mode 100644
index 0000000..dbdbf5f
--- /dev/null
+++ b/python_test/test_simplex_code.py
@@ -0,0 +1,44 @@
+import pytest
+import numpy as np
+from ldpc.codes.hamming_code import hamming_code
+from ldpc.codes.simplex_code import simplex_code
+
+def test_simplex_code_m3():
+    m = 3
+    H_simplex_actual = simplex_code(m)
+    expected_H_simplex_m3 = np.array([
+        [1, 1, 1, 0, 0, 0, 0],
+        [0, 1, 1, 1, 1, 0, 0],
+        [0, 1, 0, 1, 0, 1, 0],
+        [0, 0, 1, 1, 0, 0, 1]
+    ], dtype=np.uint8) # Use uint8 for binary matrices
+
+    # Check if matrices are equal
+    assert np.array_equal(H_simplex_actual.toarray(), expected_H_simplex_m3)
+    # Check dimensions
+    assert H_simplex_actual.shape == (4, 7) # Based on the example given
+
+def test_simplex_code_duality():
+    """Tests the duality property: H_hamming @ H_simplex.T = 0"""
+    for m_val in [3, 4, 5]: # Test for a few small values of m
+        H_hamming = hamming_code(m_val)
+        H_simplex = simplex_code(m_val)
+
+        # Perform matrix multiplication over GF(2)
+        # scipy.sparse matrices support matrix multiplication
+        result = (H_hamming @ H_simplex.transpose()).toarray() % 2
+
+        # All elements should be zero
+        assert np.all(result == 0), f"Duality check failed for m={m_val}"
+
+def test_simplex_code_dimensions():
+    """Tests if the output matrix has the correct dimensions."""
+    for m_val in [2, 3, 4, 5]:
+        H_simplex = simplex_code(m_val)
+        n = 2**m_val - 1 # Length of the code
+        #The dimension of the parity check matrix of the simplex code
+        # should be ( (2^m - 1) - m ) x (2^m - 1).
+        expected_rows = (2**m_val - 1) - m_val
+        expected_cols = 2**m_val - 1
+        assert H_simplex.shape == (expected_rows, expected_cols), \
+            f"Dimension mismatch for m={m_val}: Expected ({expected_rows}, {expected_cols}), got {H_simplex.shape}"
diff --git a/src_python/ldpc/codes/__init__.py b/src_python/ldpc/codes/__init__.py
index 7bba6a8..bb87ee3 100644
--- a/src_python/ldpc/codes/__init__.py
+++ b/src_python/ldpc/codes/__init__.py
@@ -1,3 +1,4 @@
 from ldpc.codes.rep_code import rep_code, ring_code
 from ldpc.codes.hamming_code import hamming_code
 from ldpc.codes.random_binary_code import random_binary_code
+from ldpc.codes.simplex_code import simplex_code
diff --git a/src_python/ldpc/codes/simplex_code.py b/src_python/ldpc/codes/simplex_code.py
new file mode 100644
index 0000000..003591c
--- /dev/null
+++ b/src_python/ldpc/codes/simplex_code.py
@@ -0,0 +1,36 @@
+import numpy as np
+from ldpc.codes import hamming_code
+from ldpc.mod2 import kernel
+import scipy.sparse
+
+def simplex_code(m: int) -> scipy.sparse.csr_matrix:
+    """
+    Outputs the parity check matrix of a binary simplex code.
+
+    Simplex codes are a family of binary linear codes that are duals of Hamming codes.
+    For a given integer m , the binary simplex code has parameters [ 2^m - 1 , m , 2^m - 1 ] .
+    These codes are notable for their large minimum distance and large autormorphism groups that are useful for compiling logic in quantum stabiliser codes.
+
+    Parameters
+    ----------
+        m (int): Dimension of the simplex code.
+
+    Returns
+    ----------
+        H_simplex (np.ndarray): Parity check matrix of shape (2^m - 1 - m, 2^m - 1).
+    
+    Raises
+    ------
+    TypeError
+        If the input variable 'dimension' is not of type 'int'.
+    """
+
+    # Implement function here
+    if not isinstance(m, int):
+        raise TypeError("The input variable 'rank' must be of type 'int'.")
+    H_hamming = hamming_code(m)
+
+    H_simplex = kernel(H_hamming)
+
+
+    return H_simplex
\ No newline at end of file