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In this question, we are going to construct a ( 7 , 3 ) linear block code by extending a ( 6 , 3 )

In this question, we are going to construct a (7,3) linear block code by extending a (6,3) linear block
code. The generator matrix of the (6,3) code is
G =
100110
010101
001011
The (7,3) code is extended from the (6,3) code by appending one extra bit to into the codeword such
that the Hamming weight of the resulting codeword is even. For example, for an input information sequence of [111], the (6,3) code produces an codeword of [111000] which is then extended by appending
an extra bit 1 at the end to form the final codeword of [1110001]. The reason for appending a bit 1
(instead of bit 0) is to make the Hamming weight of the resulting codeword in this example be an
even number.
Another way to describe the (7,3) code would be that it consists of a (6,3) code with generator matrix
G followed by another single parity check code with even parity
b) What is the generator matrix of this (7,3) code?

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