# operations valid for predicting new codewords for a Linear block code having linear encoder mapping

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?

• The codeword is the modulo-2 product of the dataword with a code generator matrix. This product is defined in terms of modulo-2 addition (XOR). Replacing the XOR with other operations does not make sense in this context. – MBaz Feb 24 at 20:25

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