) 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)

Let  and  be two binary codes with generator matrices

respectively.

i) Find the minimum distance of both the codes.

Table 1: Table for F₁₆.

ii) Find the generator matrix of the code

obtained from C1 and C2 by (u|u+v) construction. Also, find the minimum distance of C .

Let  and  be two binary codes with generator matrices

respectively.

i) Find the minimum distance of both the codes.

Table 1: Table for F₁₆.

ii) Find the generator matrix of the code

obtained from C1 and C2 by (u|u+v) construction. Also, find the minimum distance of C .

Find the parity check matrix of the code .

 Find the parity check matrix of the code . Decode the following vectors
i) 
ii) 
iii) 
iv) 

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 ? 

For each of the linear codes, find the degree, a generator matrix and a parity check matrix. 

 Find the minimum distance for each of the codes. 

Which of the following binary codes are linear?

i)   

ii)   

Justify your answer. 

Which of the following statements are true and which are false? Justify your answer with a short proof or a counterexample. 
i) If the weight of each element in the generating matrix of a linear code is at least r, the minimum distance of the code is at least r.
ii) There is no linear self orthogonal code of odd length.
iii) There is no 3-cyclotomic coset modulo 121 of size 25.
iv) There is no duadic code of length 15 over .
v) There is no LDPC code with parameters ,  and .

 Find the optimum solution to the following transportation problem:

 A sales manager wishes to assign four sales territories to four salespersons. The salespersons differ in their ability and skills and consequently the sales expected in each territory are different. The estimates of sales per month for each sales-person in different territories are given below:

Find the optimal assignment of the four salespersons to the four different territories and the maximum monthly sales.

Obtain all the basic solutions to the following system of linear equations:

Which of the solutions are feasible? Justify.

At present a company is purchasing an item ‘x’ from outside suppliers. The assumption of unit is 10000 units/year. The cost of the item is ₹ 5 per unit and the ordering cost is estimated to be ₹ 100 per order. The cost of carrying inventory is 25%. If the consumption rate is uniform, determine the economic order quantity.

Use branch and bound method to solve the following LPP:

Minimize: Z = 4x₁ + 3x₂

Subject to the constraints:

 and are integers.

A road transport company has one reservation clerk on duty at a time. He handles information of bus schedules and make reservations. Consumers arrive at a rate of 8 per hour and the clerk can service 12 customers on an average per hour.

i) What is the average number of customers waiting for the service of the clerk?

ii) What is the average time a customer has to wait before getting service?

) A road transport company has one reservation clerk on duty at a time. He handles information of bus schedules and make reservations. Consumers arrive at a rate of 8 per hour and the clerk can service 12 customers on an average per hour.

On an average 96 patients per 24-hour a day require the services of an emergency clinic. Also on an average, a patient requires 10 minutes of active attention. Assume that the facility can handle only one emergency at a time. Suppose that it costs the clinic ₹ 100 per patient treated to obtain an average servicing time of 10 minutes, and that each minute of decrease in this average time would cost ₹ 10 per patient treated. How much would have to budgetted by the clinic to decrease the average size of the queue from 1x1/3 patients to 1/2 a patient?

i) Construct PERT network.

ii) Find the critica

Determine the EOQ and the optimal number of orders placed in a year.

ii) Determine the optimum production lot size and the average duration of the production run.

 A manufacturing company needs 2500 units of a particular item every year. The company buys it at the rate of ₹ 30 per unit. The order processing cost for this item is estimated at ₹ 15 and the cost of carrying a item in stock comes to about ₹ 4 per year. The company can manufacture this item internally. In that case it saves 20% of the price of the product. However, it estimates a set-up cost of ₹ 250 per production run. The annual production rate would be 4800 units. However, the inventory holding costs remain unchanged.