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.
A linear fractional transformation has the form [ w=\phi(z)=\frac{az+b}{cz+d}, ] where (a,b,c,d) are complex constants not all zero and (ad-bc\neq 0). Such a transformation is completely determined up to a nonzero common factor multiplying (a,b,c,d). Consider three distinct points (z_1,z_2,z_3) in the extended (z)-plane and _______ ___ ___ ______ _______ __________ __________ _______ _______ __________.
__________ ___ ____ ____ _____ ____.
_________ ____ ______ _____ ___ _______ ____ _____ ______ ________ ___.
_______ _________ _______ ______ _____.
_____ _________ _________ ______ ________ ________ ___ _________ _______ ____ _____ ____.
____ ______ _______ __________ _____ ____ ________ _______ ___ ________ _____.
________ _____ ______ _____ ________ ______ _________ ___ ____.
_______ _________ _______ ________ __________ _____ _______ ___ __________ _____ ________.
____ _______ ____ ______ _____ ____ __________ _______.
______ _________ _______ __________ ________ ___ _________ ________ ________ _______ ____.
____ _______ _______ _________ _______ ___ _____.
__________ ______ ___ ______ _________ ______ ______ __________ ____ _____ _________.
________ ______ ___ ___ ______ ______ _______.
___ ____ _____ _________ _______ ___.
________ _______ ________ ______ _________ ___ _____ ________ _________.
_______ _______ ______ __________ _________ __________ _______.
____ ________ _____ ________ ____ _________ __________.
___ ______ ___ _________ _____ ____ ____.
__________ ________ ___ ____ ________ ________ __________ __________.
_______ _____ ______ _____ ____ _____.
_______ _________ ________ _______ ________ ___ __________.
________ __________ __________ ___ __________ _______ ___ __________ _____ __________ ____ __________.
_________ ____ _______ ___ ____ _______ _____ _____ __________ _________ ______ ______.
________ _____ ______ _____ _____.
______ _______ ______ ______ ____.
____ _______ ______ _______ ________ ______ _____.
__________ _______ ________ ____ _________ ______ ____.
___ __________ _____ _______ ________.
_______.
Get Full Answer on WhatsApp
Factor x8 - 1 over . Give the generator polynomials of all cyclic codes of length eight over
.
Find the radius of convergence of the following series.
i)
ii)
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)
Find the points where the function is not analytic.
Find all the singularities of the function .
Let and
be two binary codes with generator matrices
respectively.
i) Find the minimum distance of both the codes.
Table 1: Table for F16.
| 0000 | 0 | 1000 | α³ | 1011 | α⁷ | 1110 | α¹¹ |
|---|---|---|---|---|---|---|---|
| 0001 | 1 | 0011 | α⁴ | 0101 | α⁸ | 1111 | α¹² |
| 0010 | α | 0110 | α⁵ | 1010 | α⁹ | 1101 | α¹³ |
| 0100 | α² | 1100 | α⁶ | 0111 | α¹⁰ | 1001 | α¹⁴ |
Find the parity check matrix of the code .