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Which of the statements is/are TRUE?

Select ALL that apply.

All Hamming codes are perfect.

An extended code cannot be perfect.

There exists a Ternary Hamming code of length $30$.

The most desirable value of the reliability of a binary symmetric channel is $0.5$ .

The maximum number of code words in a binary code of length $6$ in which any single error can be detected is $32$.

If the parameters of a code satisfies the sphere packing bound, then a code with those parameters exist.