I want to know which operations are valid for predicting/finding a new codeword from a set of known codewords for a linear block code having linear encoder mapping,
for eg.:
Consider a linear Hamming code (having linear encoder mapping) is used to map $4$ - bit messages to $7$ - bit codewords,
if it is known that the message $0001$ is mapped to the codeword $0000111$,
i.e,
$$0001 \, \to \, 0000111 \, \dots (i)$$
$$\& \quad 0011 \, \to \, 1100110 \, \dots (ii)$$
,then we can find out the corresponding codeword for the message $0010$ as follows:
$\because 0010 = (0001) \, \oplus \, (0011)$ , And we know EXOR is a valid operation
$$\therefore \text{codeword for } 0010 \to (0000111) \, \oplus \, (1100110) $$
$$=1100001$$
Now, can we apply any other operations (like AND , OR , EXNOR , ...) to find the corresponding message codeword?
