Solve your IGNOU Doubts

Question:

b) Draw the Tanner graph of the code L with parity check matrix $\begin{bmatrix} 1 &0 &0 &0 &1 &0 &0 &1 & 0 &1 \\0 &1 &0 &0 &1 &1 &0 &0 &1 &0 \\0 &0 &1 &0 &0 &1 &1 &0 &0 &1 \\0 &0 &0 &1 &0 &0 &1 &1 & 1 &0 \end{bmatrix}.$

c) Find the convolutional code for the message 11011. The convolutional encoder is given in Fig. 1.

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Question:

Text:"KSTYZKESLNZUV", encrypted with Vigenère cipher with key "RESULT"

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Question:

Text: "CBBGYAEBBFZCFEPXYAEBB", encrypted with affine cipher with key (7,2)

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Question:

Let $f(x)=x^{2}-x-1\in$ $Z_5[x].$ We represent the field $F_2$ by $F_2[x]/(f(x)).$ LEt us write $y=x=(f(x)).$ the table of values is given below:

i	$y^{i}$	Vector	i	$y^{i}$	Vector
0	1	(0,0,0,1)	8	$y^{2}+1$	(0,1,0,1)
1	$y$	(0,0,1,0)	9	$y^{3}+y$	(1,0,1,0
2	$y^{2}$	(0,0,1,0)	10	$y^{3}+y+1$	(0,1,1,1)
3	$y^{3}$	(1,0,0,0)	11	$y^{3}+y^{2}+y$	(1,1,1,0)
4	$y+1$	(1,0,0,0)	12	$y^{3}+y^{2}+y+1$	(1,1,1,1)
5	$y^{2}+y$	(0,1,1,0)	13	$y^{3}+y^{2}+1$	(1,1,0,1)
6	$y^{3}+y^{2}$	(1,1,0,0)	14	$y^{3}+1$	(1,0,0,1)
7	$y^{3}+y+1$	(1,0,1,1)

i) Prepare logarithm and antilogarithm tables as given in page 23 of block 1.

ii) Compute $\frac{(y^{4}+y^{2})+(y^{3}+y+1)}{(1+y^{2}+y^{4})(1+y^{3})}\: and\: \frac{y^{2}(y^{2}+y+1)}{(y^{3}+y^{2})(1+y^{5})}$ using the logarithm and antilogarithm tables.

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Question:

8) a) Let

C= $\left \{ 0000,1113,2222,3331,1313,2020,3131,0022,1131,2200,3313,0220,1333,2002,3111 \right \}$ be the-linear code. Find the Gray image of $C.$

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Question:

c) Find the generating idempotents of duadic codes of length n = 23 over $F_{3.}$ (Hint: Mimic example 6.1.7.)

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Question:

b) Let l be the $\left [ 5,2 \right ]$ ternary code generated by

$G=\begin{pmatrix} 1 &1 &0 &0 &1 \\0 &1 &0 &1 &1 \end{pmatrix}.$

Find the weight enumerato $Wl (x,y) of l.$

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Question:

7) a) Le l be the ternary $\left [ 8,3 \right ]$ narrow-sense $BCH$ code of designed distance $\delta =5,$ which has defining set $T=\left \{ 1,2,3,4,5,6 \right \}.$ Use the primitive root 8th root of unity you chose in 4a) to avoid recomputing the the table of powers. If

$g(x)=x^{5}-x^{4}+x^{3}+x^{2}-1$

Image ignouassignments-ignouacademy-com--p-doubts-42774

Figure 1: Encoder for convolutional code.

is the generator polynomial of Image ignouassignments-ignouacademy-com--p-ignou-70875 and

$y(x)=x^{7}-x^{6}-x^{4}-x^{3}$

is the received word, find the transmitted codeword.

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Question:

Over $F_{2,}\left ( 1+x \right )|\left ( x^{n} -1\right ).$ Let L be the binary cyclic code $\left ( 1+x \right )$ of lenth n. $l_{1}$ be any binary cyclic code of length n with generator polynomial g $g_{1}$ $\left ( x \right ).$

i) What is the dimension of l?

ii) Let w be subspace of $F_{2}^{n}$ containing all the vectors of even weight. Prove that W has dimension n−1. (Hint: Consider the map w $F_{2}^{n}$ → $F_{2}^{}$ given by

$w((a_{1}a_{2}....a_{n}))=a_{1}+a_{2}+...+a_{n. )$

iii) Prove that l is the vector space of all vectors in $F_{2}^{n}$ with even weight.

iv) If l $_{1}$ has only even weight codewords, what is the relationship between $(1+x)$ and $g_{1}(x)?$

v) If $l_{1}$ has some odd weight codewords, what is the relationship between $1+x$ and $g_{1}(x)?$

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Question:

Compute the DFT of the vector (−1, 3, 1, −1).

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Question:

Let ${(-1,-5),(0,-4),(1,-1)}$ and ${(-1,14),(0,7),(1,-4)}$ be the point-value representation of $h(x)$

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Question:

a) Find all the solutions of the equation $6_X\equiv 4$ (mod 114).

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Question:

c) Compute the values $(d,x,y)$ that the call $E$ $_{XTENDED}$ - $E$ $_{UCLID}$ (10117,11591) returns.

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Question:

b) When working modulo $q=17,$ how many spurious hits does the Rabin-Karp matcher encounter in the text $T=29103292566473$ when looking for the pattern $T=29103292566473$ when looking for the pattern $22?$

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Question:

a) Show the comparisons the naive string matcher makes for the pattern $P=0100$ with $01100010010100100.$

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Question:

Use Kruskal’s algorithm to find a minimal spanning tree in the graph given in Fig. 2. Image ignouassignments-ignouacademy-com--p-doubts-64253

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Question:

Show the See Answer →

Question:

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 →

Question:

) Find an optimal parenthesisation of a matrix chain product whose sequence of dimensions is (3, 5, 7, 3, 4).

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Question:

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)

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