detect (but don't correct two-bit errors in a Word16

src/Hamming.hs

@@ -65,6 +65,7 @@ instance Hamming Word16 where
 
   correctErrors c
     | isValid c         = Just c
+    | not (oddParity c) = Nothing
     | otherwise         = let
       errorFlags = map (oddParity . (c .&.))
         [0xaaaa, 0xcccc, 0xf0f0, 0xff00]

test/Hamming/Word16Spec.hs

@@ -21,7 +21,7 @@ License along with this program.  If not, see
 
 module Hamming.Word16Spec (spec) where
 
-import Data.Bits (shiftL, xor)
+import Data.Bits (shiftL, xor, (.|.))
 import Data.Word (Word16)
 
 import Hamming
@@ -68,7 +68,7 @@ correctErrorsSpec = describe "correctErrors" $ mapM_
     in it ("should be " ++ show expected) $
       actual `shouldBe` expected
   ) $ ("valid", withChkBits, Just withChkBits) :
-  singleBitErrors
+  singleBitErrors ++ doubleBitErrors
 
 singleBitErrors :: [(String, Word16, Maybe Word16)]
 singleBitErrors = map
@@ -78,6 +78,22 @@ singleBitErrors = map
     in ("bad bit " ++ show bit, code, Just withChkBits)
   ) [0..15]
 
+doubleBitErrors :: [(String, Word16, Maybe Word16)]
+doubleBitErrors =
+  [ ( \(bitA, bitB) -> let
+      mask = (1 `shiftL` bitA) .|. (1 `shiftL` bitB)
+      code = withChkBits `xor` mask
+      in
+        ( "bad bits " ++ show bitA ++ " & " ++ show bitB
+        , code
+        , Nothing
+        )
+    ) (a, b)
+  | a <- [0..14]
+  , b <- [1..15]
+  , a < b
+  ]
+
 noChkBits :: Word16
 noChkBits = 0x34c0