SHA$-3($Secure Hash Algorithm $3)$ is the latest member of the Secure Hash Algorithm family of standards, released by NIST on August $5,2015.$ Which of the following statements about SHA$-3$ are not true?

SHA$-3$ hashes messages on the basis of the Merkle$-$Damg$$rd iterating mode.

SHA$-3$ hashes messages with a Sponge Construction.

The security of SHA$-3$ depends on the permutation capacity.

A round of SHA$-3$ contains $5$ mappings.

In SHA$-3,$ only one mapping is linear, the other mappings are nonlinear.

Like SHA$-1,$ the output of SHA$-3$ has a fixed size.