Which of the following statements are true and which are false? Justify your answer with a short proof or a counterexample.
i) If the weight of each element in the generating matrix of a linear code is at least r, the minimum distance of the code is at least r.
ii) There is no linear self orthogonal code of odd length.
iii) There is no 3-cyclotomic coset modulo 121 of size 25.
iv) There is no duadic code of length 15 over .
v) There is no LDPC code with parameters ,
and
.
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Factor x8 - 1 over . Give the generator polynomials of all cyclic codes of length eight over
.
Find the maximum modulus of on the closed circular region defined by
.
Find the radius of convergence of the following series.
i)
ii)
Find the points where the function is not analytic.
If , then show that there exists a real R > 0 such that
for
.
b) Find all solutions to the equation .
Find the zeros and singularities of the function in
. Also find the residue at the poles
Evaluate , where c is the eight like figure shown in Fig. 1.
