(i) Give brief answers to the following questions.

(a) What is a stream cypher?

(b) Explain briefly why a one-time pad is safe if used only once but becomes unsafe if used many times.

(c) What is a feedback register of length $d$ ? What is a linear feedback register of length $d ?$

(d) A cypher stream is given by a linear feedback register of known length $d$. Show that, given plain text and cyphered text of length $2 d$, we can find the complete cypher stream.

(e) State and prove a similar result for a general feedback register.

(ii) Describe the construction of a Reed-Muller code. Establish its information rate and its weight