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Need to apply the Shere-Paking bound and Varshanov-Gilbert bound to know this code is linear.

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Determine whether there can exist a linear binary code with the parameters
[n,k,d]=[12,7,5]

In here we need to apply the Shere-paking bound and Varshanov-gilbert bound to know this code is linear.

I think when this code satisfies the shere-packing we do not it is a code when satisfies we know it is not a code and when it satisfies the Varshanow-Gilbert is a code and when it not satisfies the V-G we do not it is a code>

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