Find the constant c such that can be extended to be analytic at
, when
is fixed.
Let (P(z)=z^{n}+z^{n-1}+\cdots+z-n=\sum_{k=1}^{n}z^{k}-n). Then (f(z)=\dfrac{1}{P(z)}+\dfrac{c}{z-1}). At (z=1), (P(1)=n-n=0), so the first term _________ _____ _______ _____ _____ _______ ______ ______ ______ _________.
_____ _______ _________ _______ _______.
________ ________ _____ ___ _________ ____ ____ ____ _________ _________.
_________ ____ ________ ______ ______ ______.
________ ____ ________ __________ ____ __________ _________ ______ __________.
____ _____ ____ ____ _______.
_______ _______ _______ ___ _________ ________ ________ ______ _________ _____.
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Let C be a cyclic code of length eight over with generator polynomial
. Find the generator matrix of C, the generator polynomial of C and the parity check matrix of C.
Let C be the [5, 2] binary code generated by
Find the weight enumerator C of C . Use McWilliams identity to find the weight enumerator of C. Verify your answer by finding the generator matrix of C and finding the weight distribution of C.
Find the constant c such that can be extended to be analytic at
, when
is fixed.
Factor x5 - 1 over . Give the generator polynomials of all cyclic codes of length five over
.
Expand in a Laurent series valid for
i) 0 < |z - 1| < 2 and ii) 0 < |z - 3| < 2.
) For the binary, (6,3) linear code C with generator matrix
prepare a standard array for decoding. Use it to decode the vectors (1, 1, 1, 0, 1, 1), and (1, 1, 0, 1, 1, 1). \hfill (7)
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 ?