$[5$ points$]$ LFSR Keystream Computations. Let

$$

$=$

$1110$

k$=1110$ and

$$

$=$

$1101$

d$=1101.$ Consider the LFSR cipher with key

$($

$$

$,$

$$

$)$

$($k$,$d$).$ Compute by hand:

$($a$)$ The first $19$ keystream bits

$$

$1$

$$

$2$

$$

$3$

$$

$$

$19$

z

$1$

$$

z

$2$

$$

z

$3$

$$

$$z

$19$

$$

$.$

$($b$)$ The period of the keystream.