feat: add PEG base matrix constructor with shift optimization

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

model/test_density_evolution.py

@@ -131,3 +131,47 @@ class TestDegreeDistributionOptimizer:
         best_degrees, best_threshold = results[0]
         # Original staircase threshold is ~3-5 photons
         assert best_threshold < 6.0, f"Best threshold {best_threshold} should be < 6.0"
+
+
+class TestPEGBaseMatrixConstructor:
+    """Tests for the PEG base matrix constructor."""
+
+    def test_construct_matches_target_degrees(self):
+        """Constructed matrix should have the target column degrees."""
+        from density_evolution import construct_base_matrix
+        np.random.seed(42)
+        target = [7, 3, 3, 3, 2, 2, 2, 2]
+        H_base, girth = construct_base_matrix(target, z=32, n_trials=500)
+        # Check column degrees
+        for c in range(H_base.shape[1]):
+            actual_deg = np.sum(H_base[:, c] >= 0)
+            assert actual_deg == target[c], (
+                f"Col {c}: expected degree {target[c]}, got {actual_deg}"
+            )
+
+    def test_construct_has_valid_rank(self):
+        """Full H matrix should have full rank, parity submatrix should too."""
+        from density_evolution import construct_base_matrix, verify_matrix
+        np.random.seed(42)
+        target = [7, 3, 3, 3, 2, 2, 2, 2]
+        H_base, girth = construct_base_matrix(target, z=32, n_trials=500)
+        checks = verify_matrix(H_base, z=32)
+        assert checks['full_rank'], f"Full matrix rank {checks['actual_rank']} < expected {checks['expected_rank']}"
+        assert checks['parity_rank'], f"Parity submatrix not full rank"
+
+    def test_construct_encodable(self):
+        """Encoding a random info word should produce zero syndrome."""
+        from density_evolution import construct_base_matrix, verify_matrix
+        np.random.seed(42)
+        target = [7, 3, 3, 3, 2, 2, 2, 2]
+        H_base, girth = construct_base_matrix(target, z=32, n_trials=500)
+        checks = verify_matrix(H_base, z=32)
+        assert checks['encodable'], "Should be able to encode and verify syndrome=0"
+
+    def test_construct_girth_at_least_4(self):
+        """Constructed matrix should have girth >= 4."""
+        from density_evolution import construct_base_matrix
+        np.random.seed(42)
+        target = [7, 3, 3, 3, 2, 2, 2, 2]
+        H_base, girth = construct_base_matrix(target, z=32, n_trials=500)
+        assert girth >= 4, f"Girth {girth} should be >= 4"