Prove that the linear fractional transformation maps the circle
into itself. Also prove
that f(z) is conformal in .
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If is entire such that
in
then show that f has the form
where
are constants with
.
For each of the linear codes, find the degree, a generator matrix and a parity check matrix.
Expand in a Laurent series valid for
i) 0 < |z - 1| < 2 and ii) 0 < |z - 3| < 2.
Evaluate , where c is the eight like figure shown in Fig. 1.
Find the constant c such that can be extended to be analytic at
, when
is fixed.
Prepare a syndrome table for C in part a) and decode the vectors (1, 1, 1, 1, 0, 1) and (0, 1, 0, 1, 1, 1). \hfill (5)
) 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)