If $G$ and $H$ are generator and parity check matrices of a linear block code respectively, then which of the following relations is true?

G H^{T} = 0

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G = H^{T}

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G^{T} H^{T} = 0

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G H = 0

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Solution

The correct option is A $G H^{T} = 0$
For a $(n, k)$ LBC, $G H^{T} = [I_{k} P] [\begin{matrix} P I_{(n - k)} \end{matrix}] = P \oplus P = 0$

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If G and H are generator and parity check matrices of a linear block code respectively, then which of the following relations is true?

The correct option is A GHT=0For a (n,k) LBC, GHT=[Ik P][P I(n−k)]=P⊕P=0

If $G$ and $H$ are generator and parity check matrices of a linear block code respectively, then which of the following relations is true?

The correct option is A $G H^{T} = 0$
For a $(n, k)$ LBC, $G H^{T} = [I_{k} P] [\begin{matrix} P I_{(n - k)} \end{matrix}] = P \oplus P = 0$