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Yes it is a normal matrix multiplication but within Galois finite field. We have to use Galois defined operations of $+$ and $\cdot$. Example might clarify everything. Let's say we have the $b'$ vector, and it's value is $170 = 10101010b$ Just remember tat $b'_0$ is the least significant bit of that value. $b_0 = (1 \wedge b'_0) \oplus (0 \wedge b'_1) ...


This is normal matrix multiplication, but when filling in b′ remember that b′0 is the least significant bit (this is the case for the answer too). The matrix multiplication and addition will result in numbers other than 0 and 1, but using the modular 2 it will reduce to 0 and 1 only.

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