Q2) Let a be a primitive element in GF (24). Divide the polynomial f(X) = aX7...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Q2) Let a be a primitive element in GF (24). Divide the polynomial f(X) = a³X7 +aX6 + a²X4+ a²X² + a¹¹X + 1 over GF (24) by the polynomial g(X) = X¹ + a³X² +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 α¹ a² a³ 4 a a5 α6 a7 α8 α⁹ a10 a¹1 12 α a13 14 α· 0 1 Polynomial representation α a² a³ 1 + a a + a² a² + a³ 1 +a+a³ 1 + a² a + a³ 1+ a + a² a + a² + a³ 1+ a + a² + a³ 1 + a² + a³ 1 + a² 4-Tuple representation 0 1 0 0 0 1 0 اد 0 1 1 0 1 0 1 1 1 DITOOOO OOO 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 -OO 1 0 1 1 0 1 -110 0 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1 Q2) Let a be a primitive element in GF (24). Divide the polynomial f(X) = a³X7 +aX6 + a²X4+ a²X² + a¹¹X + 1 over GF (24) by the polynomial g(X) = X¹ + a³X² +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 α¹ a² a³ 4 a a5 α6 a7 α8 α⁹ a10 a¹1 12 α a13 14 α· 0 1 Polynomial representation α a² a³ 1 + a a + a² a² + a³ 1 +a+a³ 1 + a² a + a³ 1+ a + a² a + a² + a³ 1+ a + a² + a³ 1 + a² + a³ 1 + a² 4-Tuple representation 0 1 0 0 0 1 0 اد 0 1 1 0 1 0 1 1 1 DITOOOO OOO 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 -OO 1 0 1 1 0 1 -110 0 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics 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) = X4+ 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) < | sin x |, show that | a1 2a2 + . . . + na n | <...
-
An arm ABC lying in a horizontal plane and supported at A (see figure) is made of two identical solid steel bars AB and BC welded together at a right angle. Each bar is 20 in. long. Knowing that the...
-
Asian Iron began last year with no inventories. During the year, 10,500 units were produced, of which 9,400 were sold. Data concerning last years operations appear here (in New Taiwan dollars, NT$):...
-
Which is the largest component of GDP? a. consumption b. investment c. government purchases d. net exports
-
Starting with Eq. (4.1-10), show that if \(\Delta v \ll \bar{v}\) and \(r \ll 2 c / \Delta v\) for all \(P_{1}\), then \[ \mathbf{u}\left(P_{0}, t ight) \approx \iint_{\Sigma} \frac{e^{j 2 \pi(r /...
-
A group of high-risk automobile drivers (with three moving violations in one year) are required, according to random assignment, either to attend a traffic school or to perform supervised volunteer...
-
Calculate the levelized cost of heating ($/MBTU) and the emissions (tons/MBTU) for a natural gas furnace and an electric heat pump. [10 points]
-
The 2018 balance sheets and income statement for Netflix Inc. follow. Refer to these financial statements to answer the requirements. NETFLIX INC. Consolidated Statement of Earnings For Year Ended...
-
As a door supervisor at a club, you are asked to assist in the removal of an unruly patron. the young female patron was involved in a physical fight with another patron. She is now shaking her fist...
-
Just at the turn of the New Year of 2018, you have just been appointed as a Portfolio Manager and Strategic Pricing Specialist of large Asset Management Company. This company has branches in many...
-
Cool Look Limited (CLL) is a high-end clothing design and manufacturing company that has been in business in Canada since 1964. CLL started as an owner-managed enterprise created and run by Hector...
-
Find the answers to the questions below and what are the answers? What is the total personal property (after any 179)? What is the Total Personal Property 4th quarter (after any 179)?
-
Variable Costing Income Statement; Reconciliation LO6-1, LO6-2, LO6-3 During Heaton Company's first two years of operations, it reported absorption costing net operating income as follows: Year 1...
-
A property manager is hired to rent out a client's single-family home. There are two applicants that apply. The first individual is a single male who has had a job for one month and is receiving cash...
-
Calculating the future value of a cash that you have today is called: Question 3 options: Compounding. Time value of money. Discounting. Discount factor
-
Flicker, Inc., a closely held corporation, acquired a passive activity this year. Gross income from operations of the activity was $160,000. Operating expenses, not including depreciation, were...
-
Let Hn be the n à n Hilbert matrix (1.70), and Kn = H-ln its inverse. It can be proved, [32, p. 513], that the (i, j) entry of Kn is Where is the standard binomial coefficient. (a) Write down...
-
(a) Prove that if ui (t) and u2 (t) are any two distinct solutions to du/dt = au with a > 0, then |u1(t) - u2(t)| as t . (b) If a = .02 and u1(0) = .1, u2(0) = .05, how long do you have to wait...
-
Write the following polynomials as linear combinations of monic Legendre polynomials. Use orthogonality to compute the coefficients: (a) t3 (b) t4 + t2 (c) 7t4 + 2t3 - t
-
A \(15.0-\mathrm{kg}\) block measures \(0.750 \mathrm{~m}\) top to bottom, and each horizontal face has an area of \(0.0125 \mathrm{~m}^{2}\). The block hangs, with its long central axis vertical,...
-
A hydrogen-filled balloon is used to lift a \(125-\mathrm{kg}\) stone off the ground. The basket holding the stone has a mass of \(15.0 \mathrm{~kg}\). What must the minimum radius \(R\) of the...
-
At an atmospheric pressure of \(1.00 \mathrm{~atm}\), the height of the liquid in the tube of a mercury barometer is \(760 \mathrm{~mm}\) only if you ignore capillary rise in the tube. Obtain an...
Study smarter with the SolutionInn App