Question: Q2) Let a be a primitive element in GF (24). Divide the polynomial f(X) = aX7 +aX6 + aX4+ aX + aX + 1

Q2) Let a be a primitive element in GF (24). Divide the polynomial f(X) = aX7 +aX6 + aX4+ aX + ax + 1 over GF

Q2) Let a be a primitive element in GF (24). Divide the polynomial f(X) = aX7 +aX6 + aX4+ aX + aX + 1 over GF (24) by the polynomial g(X) = X4+ aX + a5X + 1 over GF (24). Find the quotient and the remainder (use Table 1) Table 1: Three representations for the elements in GF (24) generated by p(X) = 1 + X+X4. Power representation 0 1 a q a a4 as 6 a7 a8 a a 10 a11 a . 12 a13 a4 0 1 Polynomial representation a a 1 + a a + a a + a 1+a+a 1 + a a + a 1 +a+a a + a + a 1+a+a + a 1 + a +a 1 + a 4-Tuple representation 0 0 00 1 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 1 0 blo 0 1 1 0 1 0 1 1 1 1 1 0 0 0 oooo 0 0 0 1 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1001

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The task at hand involves dividing the polynomial fX 3X7 X6 7X4 2X2 11X 1 over GF24 by the polynomial gX X4 3X2 5X 1 also over GF24 Since the arithmet... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Electrical Engineering Questions!

Let a be a primitive element in GF(24). Use Table 2.8 to solve the following simultaneous equations for X. Y, and Z: X +aY + Z =a", X + aY +a7z =a, aX + Y +aZ = . TABLE 2.8: Three representations for...

Q2) Let a be a primitive element in GF (24). Divide the polynomial f(X) = aX7 +aX6 + aX4+ aX + aX + 1 over GF (24) by the polynomial g(X) = X + aX +a5X + 1 over GF (24). Find the quotient and the...

Let f(x) = a1 sin x + a2 sin 2x + . . . + an, where a1, a2, . . .an, are real numbers and is a positive integer. If it is given that for all | f(x)

In order to initiate a process operation, an infrared motion sensor (radiation detector) is employed to determine the approach of a hot part on a conveyor system. To set the sensor's amplifier...

The object of this problem is to illustrate how the armature windings of certain machines, i.e., dc machines, can be approximately represented by uniform current sheets, the degree of correspondence...

In our Nodhead example, true depreciation was decelerated. That is not always the case. For instance, figure shows how on average the value of a Boeing 737 has varied with its age. 28 Table 12.11...

Use the data in Table 10.4 to compute a five- day moving average for Computers, Inc. Can you identify any buy or sell signals? TABLE 10.4 Computers, Inc. Stock Price History Trading Computers,...

The data processing department of the Arizona Bank has five data entry clerks. Each working day their supervisor verifies the accuracy of a random sample of 250 records. A record containing one or...

The percentage of heights greater than 156 centimeters use the normal distribution of heights of adult women, which has a mean of 162 centimeters and a standard deviation of 6 centimeters. Use Table...

Emergency calls to the 911 system of Durham, North Carolina, for the past 24 weeks are shown in the following table: a) Compute the exponentially smoothed forecast of calls for each week. Assume an...

You are the controller for Foxboro Technologies. Your staff has prepared an income statement for the current year and has developed the following additional information by analyzing changes in the...

Top managers of OHare Products, Inc., have asked for your help in comparing the companys profit performance and financial position with the average for the industry. The accountant has given you the...

Determine whether Converges or disterges of ther therorm. 1 1 1 x 2 d x .

If a compressive force of 3.6 X 104 N is exerted on the end of a 22-cm-long bone of cross-sectional area 3.6 cm2, (a) Will the bone break, and (b) If not, by how much does it shorten?

Knowing that WA = 40lb, WB = 52 lb, and Î¸ =25°, determine (a) Whether the system is in equilibrium, (b) The magnitude and direction of the friction force. H, =0.35 H =0.25

Determine the internal normal force, shear force, and moment acting at points B and C on the curved rod. Units Used: kip = 103 lb Given: F = 500 lb 2 = 30 deg r = 2 ft a = 3 1 = 45 deg b = 4 - NB M

A bead slides without friction around a loop-the-loop (Fig. P8.5). The bead is released from a height h = 3.50R. (a) What is its speed at point A? (b) How large is the normal force on it if its mass...

As an astronaut, you observe a small planet to be spherical. After landing on the planet, you set off, walking always straight ahead, and find yourself returning to your spacecraft from the opposite...

Project Planning (Phase 1) You are a project manager. You have been assigned the following mini-project. A doctor's office is requesting a new basic website. They are a new office and have just...

True or false: If A B = 0 then either A = O or B = 0.

Let L1: U v1 and L2: U V2 be linear maps between inner product spaces, with V1, V2 not necessarily the same. Let K1 = L1* L1, K2 = L2* L2. Show that the sum K = K1 + K2 can be written as a...

Let z be the n Ã 1 column vector all of whose entries are equal to 1. (a) Show that if A is an m Ã n matrix, the ith entry of the product v = Az is the ith row sum of A, meaning the sum...

Bach Photographs is a photography business with studios in two locations. The owner is interested in monitoring business activity closely at the two locations. Among the factors in which he is...

A student group at a university located in the Midwest is conducting a study to determine whether there is a difference between textbook prices for new textbooks sold by the on-campus bookstore and...

Amax Industries operates two manufacturing facilities that specialize in doing custom manufacturing work for the semiconductor industry. The facility in Denton, Texas, is highly automated, whereas...