Find all the singularities of the function .

 Evaluate the following integrals

a) .
b) .

 Find the parity check matrix of the code . Decode the following vectors
i) 
ii) 
iii) 
iv) 

For a linear code C with generator matrix

find the parity check matrix. Check that any two columns of the parity check matrix are linearly independent and there are three columns that are linearly dependent. What is the minimum distance of C ? 

 Show that there is only one linear fractional transformation that maps three given distinct points z₁, z₂ and z₃ in the extended z plane onto three specified distinct points w₁, w₂ and w₃ in the extended w plane.

Find the parity check matrix of the code .

For each of the linear codes, find the degree, a generator matrix and a parity check matrix.