diff --git a/src/qiskit_qec/circuits/repetition_code.py b/src/qiskit_qec/circuits/repetition_code.py
index 89a93cc1..f507b1da 100644
--- a/src/qiskit_qec/circuits/repetition_code.py
+++ b/src/qiskit_qec/circuits/repetition_code.py
@@ -634,6 +634,8 @@ def _get_cycles(self):
         self.degree = {}
         for n, q in enumerate(self.link_graph.nodes()):
             self.degree[q] = self.link_graph.degree(n)
+        degrees = list(self.degree.values())
+        self._linear = degrees.count(1) == 2 and degrees.count(2) == len(degrees) - 2
         lg_edges = set(self.link_graph.edge_list())
         lg_nodes = self.link_graph.nodes()
         ng = nx.Graph()
@@ -1360,8 +1362,11 @@ def is_cluster_neutral(self, atypical_nodes: dict):
         Args:
             atypical_nodes: dictionary in the form of the return value of string2nodes
         """
-        neutral, logicals, _ = self.check_nodes(atypical_nodes)
-        return neutral and not logicals
+        if self._linear:
+            return not bool(len(atypical_nodes) % 2)
+        else:
+            neutral, logicals, _ = self.check_nodes(atypical_nodes)
+            return neutral and not logicals
 
     def transpile(self, backend, echo=("X", "X"), echo_num=(2, 0)):
         """
diff --git a/test/code_circuits/test_rep_codes.py b/test/code_circuits/test_rep_codes.py
index 7a76430c..8afb6fba 100644
--- a/test/code_circuits/test_rep_codes.py
+++ b/test/code_circuits/test_rep_codes.py
@@ -513,15 +513,18 @@ def clustering_decoder_test(
         N = 1000
 
         # first an RCC
-        codes = [RepetitionCode(d, 1)]
+        codes = []
+        codes.append(RepetitionCode(d, 1))
         # then a linear ARC
         links = [(2 * j, 2 * j + 1, 2 * (j + 1)) for j in range(d - 1)]
         codes.append(ArcCircuit(links, 0, logical="1"))
+        self.assertTrue(codes[-1]._linear, "Linear ARC not recognised as such")
         # then make a bunch of non-linear ARCs
         links_cross = [(2 * j, 2 * j + 1, 2 * (j + 1)) for j in range(d - 2)]
         links_cross.append((2 * (d - 2), 2 * (d - 2) + 1, 2 * (int(d / 2))))
         links_cross.append(((2 * (int(d / 2))), 2 * (d - 1), 2 * (d - 1) + 1))
         codes.append(ArcCircuit(links_cross, 0))
+        self.assertTrue(not codes[-1]._linear, "Non-inear ARC not recognised as such")
         # ladder (works for even d)
         half_d = int(d / 2)
         links_ladder = []