Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 3 / 3K / a

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- Solution a

Solution

For binary length-

n

C_{2} \subseteq C_{1}

, their bar product of binary linear codes is

C_{1} ∣ C_{2} = {(u, u + v) : u \in C_{1}, v \in C_{2}} .

It is a binary linear code of length

2 n

dim C_{1} + dim C_{2}

.

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