Add message decode with Reed-Solomon

The decode works like that :
- Parse each combination of points possible (exclude the correct points)
- Create a sublist of points with all corrects points and the current
combination of points
- Create the lagrange polynomial with the sublist of points
- Parse each points to verify if the polynomial is correct
- Pass the x value of each points through the lagrange polynomial
- If the result is the same that the y value, then the point is correct
- Verify if we have enough valid points, so it must be equal or higher
than m + n points
- Decode the message

polynomial.py

@@ -146,24 +146,40 @@ def compute_lagrange_polynomial(points, prime_number):
 
 
 def reed_solomon(points, data_length, last_error_index, prime_number):
+    combination_length = data_length - len(points[:last_error_index])
+
+    # Parse each combination of points possible (exclude the correct points)
+    for x in itertools.combinations(points[: last_error_index + 1], combination_length):
+        nb_valid_points = 0
+        # Create a sublist of points with all corrects points and the current combination of points
+        sub_points = list(x) + points[last_error_index + 1:]
+
+        # Create the lagrange polynomial with the sublist of points
+        lagrange = compute_lagrange_polynomial(sub_points, prime_number)
+
+        # Parse each points to verify if the polynomial is correct
+        for p in points:
+            x = p[0]
+            # Pass the x value of each points through the lagrange polynomial
+            y = lagrange.pass_x_throughout(x) % prime_number
+            # If the result is the same that the y value, then the point is correct
+            if y == p[1]:
+                nb_valid_points += 1
+
+        # Verify if we have enough valid points, so it must be equal or higher than m + n points
+        if nb_valid_points >= data_length + (len(points) - data_length) // 2:  # // = euclid division
+            # Decode the message
+            output = ''
+            for i in range(data_length):
+                output += chr(lagrange.pass_x_throughout(i) % prime_number)
+
+            return output
+
     return None
 
 
 def main():
-    # m + 2n
-    # 25 + 2 * 11 = 47
     message = {"data_length": 25, "last_error_index": 23, "prime_number": 401, "points": [67, 101, 38, 109, 101, 115, 133, 118, 103, 128, 62, 118, 97, 156, 116, 77, 49, 56, 86, 112, 171, 105, 176, 116, 115, 183, 30, 315, 368, 29, 352, 54, 333, 198, 139, 234, 321, 92, 5, 272, 396, 265, 397, 386, 229, 153, 276]}
-    # > 23 => 24 à 46 = 23 points
-    # Il faut trouver 2 points dans [0 ; 23]
-    print(len(message["points"]))
-    print(message["points"][: 23 + 1])
-    print(message["points"][23 + 1 :])
-    # 25 points
-    # Polynome qui passe les 25 points possiblement juste
-    # On test tous les points, si le polynome passe par m + n points c'est le bon
-    # 0 à 24
-    # 0, 1, 2, 3
-
     points = [(x, y) for x, y in enumerate(message["points"])]
     print(points)
     corrected_data = reed_solomon(points, message["data_length"], message["last_error_index"], message["prime_number"])