7) a) Le l be the ternary narrow-sense
code of designed distance
which has defining set
Use the primitive root 8th root of unity you chose in 4a) to avoid recomputing the the table of powers. If
Figure 1: Encoder for convolutional code.
is the generator polynomial of and
is the received word, find the transmitted codeword.
See Answer →Over Let L be the binary cyclic code
of lenth n.
be any binary cyclic code of length n with generator polynomial g
i) What is the dimension of l?
ii) Let w be subspace of containing all the vectors of even weight. Prove that W has dimension n−1. (Hint: Consider the map w
→
given by
iii) Prove that l is the vector space of all vectors in with even weight.
iv) If l has only even weight codewords, what is the relationship between
and
v) If has some odd weight codewords, what is the relationship between
and
Compute the DFT of the vector (−1, 3, 1, −1).
See Answer →Let and
be the point-value representation of
a) Find all the solutions of the equation (mod 114).
c) Compute the values that the call
-
(10117,11591) returns.
b) When working modulo how many spurious hits does the Rabin-Karp matcher encounter in the text
when looking for the pattern
when looking for the pattern
a) Show the comparisons the naive string matcher makes for the pattern with
Use Kruskal’s algorithm to find a minimal spanning tree in the graph given in Fig. 2.
Show the See Answer →
a) In the Coin changing problem, we have to give change for n rupees using the least number of coins of a given set of denominations. It is clear that we cannot give change for any See Answer →
) Find an optimal parenthesisation of a matrix chain product whose sequence of dimensions is (3, 5, 7, 3, 4).
See Answer → For the following set of points, describe how the closest-pair algorithm finds a closest pair of
points:
(3, 2), (2, 1), (2, 3), (1, 2), (3, 1), (2, 2), (1, 3), (3, −1), (5, −2)
Show how mergesort sorts the array See Answer →
a) Show the results of inserting the keys
See Answer →
Discuss five types of infectious diseases caused by microbes. Add a note on the spread or transmission of these diseases.
See Answer →What is mass communication? Discuss the technological advances in mass communication.
See Answer →Explain the concept of chemical evolution with the help of Miller’s experiment.
See Answer →Explain the application of science and technology in small scale industries.
See Answer →