Undetectable error correcting codes I have a 256 bit string (indistinguishable from random) which I wish to encode into a greater length string using an error correction code.

The result must also be indistinguishable from random. It should not be possible to detect the presence of error correction from the result.

Is it possible? And if so, how?

PS: Related: https://crypto.stackexchange.com/questions/80890/error-correcting-codes-that-are-indistinguishable-from-random
One natural approach is to apply the error-correcting code, then encrypt the codeword with a stream cipher (e.g., AES-CTR mode).  The recipient can decrypt (this will not increase the number of bits with an error), then decode the code to correct any errors.  Anyone who does not know the symmetric key will be unable to distinguish the transmitted ciphertext from a random string.