The JCE ciphers are usually very basic. If you need a full featured protection including integrity and key testing, you need to combine them. And as usual it is better to not device that yourself. So better opt for a more high level format like PKCS7/12 or PGP.
Depending on the Padding used some ciphers will give you a PaddingException when you try to decrypt it with the wrong key. For stronger integrity check I would use a padding consiting of HMAC bytes.
A pretty complete method is included in the JCE, it is the AESWrap algorithm. It requires padded data but will ensure integrity. It is best combined with a length byte as described in RFC 3537. Note, that this is only intended for smaller amounts of secrets (like symmetric keys). The RFC3537 padding is restricted to 255 bytes.
To use this with a password derived key, you can use this:
char[] pass = ... // your password
byte[] codeBytes = ... // up to 255 bytes you want to protect
// generate wrapping key from password
SecretKeyFactory f = SecretKeyFactory.getInstance("PBKDF2WithHmacSHA1");
SecureRandom rand = SecureRandom.getInstance("SHA1PRNG");
byte[] salt = new byte[16]; rand.nextBytes(salt);
SecretKey kek = f.generateSecret(new PBEKeySpec(pass, salt, 1000, 128));
kek = new SecretKeySpec(password.getEncoded(), "AES"); // convert into AES
// RFC3537 padding (lengthbyte)
byte[] wrappedCodeBytes = new byte[codeBytes + 1 % 8];
System.arraycopy(codeBytes,0,wrappedCodeBytes,1,wrappedCodeBytes.length);
paddedCodeBytes[0]=(byte)codeBytes.length;
byte[] pad = new byte[paddedCodeBytes.length - codeBytes.length -1]; rand.nextBytes(pad);
System.arraycopy(pad,0,paddedCodeBytes,codeBytes.length+1,pad.length);
// AESWrap is WRAP_MODE:needs a SecretKey
SecretKey paddedCodeKey = new SecretKeySpec(paddedCodeBytes, "RAW");
// now wrap the password with AESWrap kek is 128 bit
Cipher c = Cipher.getInstance("AESWrap"); // default IV
c.init(Cipher.WRAP_MODE, kek);
byte[] result = c.warp(paddedCodeKey);
The unwrapping is left for the reader as an exercise :) The example code uses 128bit keysize, since more entropy cant be expected from the PBKDF2 anyway.
Note that this will detect wrong passwords with high probability, and some critics will see this as a weakness of AESWrap.