Question

Information and theory coding

Question : Show that C={000,111} is a linear code.

Answer 1

A linear code is a code in which the sum (mod 2) of any two codewords is also a codeword. That is, C is linear iff for any pair of codewords v, w $\in$ C, we also have v + w $\in$ C.

So,here C={000,111}

000 + 000 = 000 $\in$ C.

000 + 111 = 111 $\in$ C.

111 + 111 = 000 $\in$ C.

So,  C={000,111} is linear code.