) Evaluate the following integrals:
i) .
ii) .
Let (f) be analytic on and inside the unit circle and write its Taylor expansion ___ ___ _______ ________ ________ _______ ________ ________ ________ _______.
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Factor x5 - 1 over . Give the generator polynomials of all cyclic codes of length five over
.
) Evaluate the following integrals:
i) .
ii) .
If , then show that there exists a real R > 0 such that
for
.
b) Find all solutions to the equation .
he aim of this exercise is to show that every binary repetition code of odd length is perfect.
i) Find the value of t and d for a binary repetition code of length . \hfill (2)
ii) Show that
(Hint: Start with the relation
iii) Deduce that every repetition code of odd length is perfect.
For each of the linear codes, find the degree, a generator matrix and a parity check matrix.
Find all the singularities of the function .
Find the minimum distance for each of the codes.