diff --git a/include/xor_codes/xor_hd_code_defs.h b/include/xor_codes/xor_hd_code_defs.h
index 64468a2..df15e80 100644
--- a/include/xor_codes/xor_hd_code_defs.h
+++ b/include/xor_codes/xor_hd_code_defs.h
@@ -34,6 +34,9 @@ unsigned int g_12_6_4_hd_code_data_bms[] = { 7, 14, 28, 56, 49, 35, 13, 26, 52,
 unsigned int g_10_5_3_hd_code_parity_bms[] = { 163, 300, 337, 582, 664 };
 unsigned int g_10_5_3_hd_code_data_bms[] = { 5, 9, 10, 18, 20, 3, 12, 17, 6, 24 };
 
+unsigned int g_3_3_3_hd_code_parity_bms[] = { 5, 6, 3 };
+unsigned int g_3_3_3_hd_code_data_bms[] = { 5, 6, 3};
+
 
 // The rest were generated via the "goldilocks" code algorithm
 unsigned int g_6_6_3_hd_code_parity_bms[] = { 3, 48, 36, 24, 9, 6 };
@@ -123,10 +126,13 @@ unsigned int * hd3_m5_data[11] = { 0, 0, 0, 0, 0, g_5_5_3_hd_code_data_bms, g_6_
 unsigned int * hd3_m6_parity[16] = { 0, 0, 0, 0, 0, 0, g_6_6_3_hd_code_parity_bms, g_7_6_3_hd_code_parity_bms, g_8_6_3_hd_code_parity_bms, g_9_6_3_hd_code_parity_bms, g_10_6_3_hd_code_parity_bms, g_11_6_3_hd_code_parity_bms, g_12_6_3_hd_code_parity_bms, g_13_6_3_hd_code_parity_bms, g_14_6_3_hd_code_parity_bms, g_15_6_3_hd_code_parity_bms };
 unsigned int * hd3_m6_data[16] = { 0, 0, 0, 0, 0, 0, g_6_6_3_hd_code_data_bms, g_7_6_3_hd_code_data_bms, g_8_6_3_hd_code_data_bms, g_9_6_3_hd_code_data_bms, g_10_6_3_hd_code_data_bms, g_11_6_3_hd_code_data_bms, g_12_6_3_hd_code_data_bms, g_13_6_3_hd_code_data_bms, g_14_6_3_hd_code_data_bms, g_15_6_3_hd_code_data_bms };
 
+unsigned int * hd3_m3_parity[4] = { 0, 0, 0, g_3_3_3_hd_code_parity_bms };
+unsigned int * hd3_m3_data[4] = { 0, 0, 0, g_3_3_3_hd_code_data_bms };
+
 unsigned int ** parity_bm_hd4 [7] = { 0, 0, 0, 0, 0, hd4_m5_parity, hd4_m6_parity };
 unsigned int ** data_bm_hd4 [7] = { 0, 0, 0, 0, 0, hd4_m5_data, hd4_m6_data };
-unsigned int ** parity_bm_hd3 [7] = { 0, 0, 0, 0, 0, hd3_m5_parity, hd3_m6_parity };
-unsigned int ** data_bm_hd3 [7] = { 0, 0, 0, 0, 0, hd3_m5_data, hd3_m6_data };
+unsigned int ** parity_bm_hd3 [7] = { 0, 0, 0, hd3_m3_parity, 0, hd3_m5_parity, hd3_m6_parity };
+unsigned int ** data_bm_hd3 [7] = { 0, 0, 0, hd3_m3_data, 0, hd3_m5_data, hd3_m6_data };
 
 #define PARITY_BM_ARY(k, m, hd) (hd == 3) ? parity_bm_hd3[m][k] : parity_bm_hd4[m][k]
 #define DATA_BM_ARY(k, m, hd) (hd == 3) ? data_bm_hd3[m][k] : data_bm_hd4[m][k]
diff --git a/src/builtin/xor_codes/xor_hd_code.c b/src/builtin/xor_codes/xor_hd_code.c
index d34e2d3..5c4d052 100644
--- a/src/builtin/xor_codes/xor_hd_code.c
+++ b/src/builtin/xor_codes/xor_hd_code.c
@@ -664,6 +664,8 @@ xor_code_t* init_xor_hd_code(int k, int m, int hd)
       if (k <= 10 && k >= 5) {
         is_valid = 1;
       }
+    } else if (m == 3) {
+      is_valid = 1;
     }
   }
   
diff --git a/test/builtin/xor_codes/test_xor_hd_code.c b/test/builtin/xor_codes/test_xor_hd_code.c
index 497b052..f40621b 100644
--- a/test/builtin/xor_codes/test_xor_hd_code.c
+++ b/test/builtin/xor_codes/test_xor_hd_code.c
@@ -238,6 +238,11 @@ int run_test(int k, int m, int hd)
   fprintf(stderr, "Running (%d, %d, %d):\n", k, m, hd);
   
   switch(k+m) {
+    case 6:
+      if (hd == 3) {
+        ret = test_hd_code(code_desc, NUM_6_3_COMBS, failure_combs_6_3);
+      }
+      break;
     case 10:
       if (hd == 3) {
         ret = test_hd_code(code_desc, NUM_10_3_COMBS, failure_combs_10_3);
@@ -348,6 +353,11 @@ int main()
 {
   int ret = 0;
   int i;
+
+  ret = run_test(3, 3, 3);
+  if (ret != 0) {
+    return ret;
+  }
  
   for (i=6; i < 16; i++) {
     ret = run_test(i, 6, 3);
diff --git a/test/builtin/xor_codes/test_xor_hd_code.h b/test/builtin/xor_codes/test_xor_hd_code.h
index eb96d05..9a1676f 100644
--- a/test/builtin/xor_codes/test_xor_hd_code.h
+++ b/test/builtin/xor_codes/test_xor_hd_code.h
@@ -22,6 +22,8 @@
  * ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  */
 
+#define NUM_6_3_COMBS 21
+int failure_combs_6_3[NUM_6_3_COMBS][4] =  {{0, -1, -1, -1}, {1, -1, -1, -1}, {2, -1, -1, -1}, {3, -1, -1, -1}, {4, -1, -1, -1}, {5, -1, -1, -1}, {0, 1, -1, -1}, {0, 2, -1, -1}, {0, 3, -1, -1}, {0, 4, -1, -1}, {0, 5, -1, -1}, {1, 2, -1, -1}, {1, 3, -1, -1}, {1, 4, -1, -1}, {1, 5, -1, -1}, {2, 3, -1, -1}, {2, 4, -1, -1}, {2, 5, -1, -1}, {3, 4, -1, -1}, {3, 5, -1, -1}, {4, 5, -1, -1}} ;
 #define NUM_10_3_COMBS 55
 int failure_combs_10_3[NUM_10_3_COMBS][4] =  {{0, -1, -1, -1}, {1, -1, -1, -1}, {2, -1, -1, -1}, {3, -1, -1, -1}, {4, -1, -1, -1}, {5, -1, -1, -1}, {6, -1, -1, -1}, {7, -1, -1, -1}, {8, -1, -1, -1}, {9, -1, -1, -1}, {0, 1, -1, -1}, {0, 2, -1, -1}, {0, 3, -1, -1}, {0, 4, -1, -1}, {0, 5, -1, -1}, {0, 6, -1, -1}, {0, 7, -1, -1}, {0, 8, -1, -1}, {0, 9, -1, -1}, {1, 2, -1, -1}, {1, 3, -1, -1}, {1, 4, -1, -1}, {1, 5, -1, -1}, {1, 6, -1, -1}, {1, 7, -1, -1}, {1, 8, -1, -1}, {1, 9, -1, -1}, {2, 3, -1, -1}, {2, 4, -1, -1}, {2, 5, -1, -1}, {2, 6, -1, -1}, {2, 7, -1, -1}, {2, 8, -1, -1}, {2, 9, -1, -1}, {3, 4, -1, -1}, {3, 5, -1, -1}, {3, 6, -1, -1}, {3, 7, -1, -1}, {3, 8, -1, -1}, {3, 9, -1, -1}, {4, 5, -1, -1}, {4, 6, -1, -1}, {4, 7, -1, -1}, {4, 8, -1, -1}, {4, 9, -1, -1}, {5, 6, -1, -1}, {5, 7, -1, -1}, {5, 8, -1, -1}, {5, 9, -1, -1}, {6, 7, -1, -1}, {6, 8, -1, -1}, {6, 9, -1, -1}, {7, 8, -1, -1}, {7, 9, -1, -1}, {8, 9, -1, -1}} ;
 #define NUM_10_4_COMBS 175
diff --git a/test/liberasurecode_test.c b/test/liberasurecode_test.c
index 548d070..6291be5 100644
--- a/test/liberasurecode_test.c
+++ b/test/liberasurecode_test.c
@@ -58,9 +58,9 @@ struct ec_args null_args = {
 };
 
 struct ec_args flat_xor_hd_args = {
-    .k = 10,
-    .m = 6,
-    .hd = 4,
+    .k = 3,
+    .m = 3,
+    .hd = 3,
     .ct = CHKSUM_NONE,
 };