Let EF256, let be a primitive element of E, and let a = 35. Note that...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Let EF256, let be a primitive element of E, and let a = 35. Note that the order of a is 51 (i.e., you are given this fact and do not need to check it or justify it). Let C be the BCH code based on a with designed distance = 5 over F2. In the following, show all your work, especially your orbit calculations. (a) Recall that mi(x) is the minimal polynomial of a. Express m(x) as a product of terms of the form (x - a). (b) Find the generating polynomial g(x) of C, expressed as a product of minimal polyno- mials m(x). (You do not need to expand each mi (r) as a product of terms of the form (x-a), other than the expansion of m(x) that you have already done in part (a).) (c) Find kdim C. 14. (24 points) Fix N = 36 and w = 2/36. Let Ho= C, H = C2, H2 = C6, H3 = C12, and H4 =C36. Recall that the main loop of the FFT based on C < C2 < C6 < C12 C36: f(0) applied to the initial input x = can be described as follows. For i = 1 to 4: [f(N-1)] == Set H-1 = (w), H = (wk), and d = m/k. d-1 Subgroup fill: For j = 0 to (N/k) 1, set y(jk) = x(jm + kr)wrkj T=0 Translate the subgroup fill to cosets of Hi, set x = y, and loop. (a) Working in terms of w, write out the elements of H2 and H3 and write out the elements of the standard transversal T2,3 for H2 in H3. (b) Write out the results of the "subgroup fill" part of step 3 (i = 3). That is, for all t corresponding to the elements of H3, write out the formula for y(t) in terms of the inputs x (the output of step 2, i = 2). (c) Draw the corresponding subgroup subdiagram for step 3 (i = 3). Let EF256, let be a primitive element of E, and let a = 35. Note that the order of a is 51 (i.e., you are given this fact and do not need to check it or justify it). Let C be the BCH code based on a with designed distance = 5 over F2. In the following, show all your work, especially your orbit calculations. (a) Recall that mi(x) is the minimal polynomial of a. Express m(x) as a product of terms of the form (x - a). (b) Find the generating polynomial g(x) of C, expressed as a product of minimal polyno- mials m(x). (You do not need to expand each mi (r) as a product of terms of the form (x-a), other than the expansion of m(x) that you have already done in part (a).) (c) Find kdim C. 14. (24 points) Fix N = 36 and w = 2/36. Let Ho= C, H = C2, H2 = C6, H3 = C12, and H4 =C36. Recall that the main loop of the FFT based on C < C2 < C6 < C12 C36: f(0) applied to the initial input x = can be described as follows. For i = 1 to 4: [f(N-1)] == Set H-1 = (w), H = (wk), and d = m/k. d-1 Subgroup fill: For j = 0 to (N/k) 1, set y(jk) = x(jm + kr)wrkj T=0 Translate the subgroup fill to cosets of Hi, set x = y, and loop. (a) Working in terms of w, write out the elements of H2 and H3 and write out the elements of the standard transversal T2,3 for H2 in H3. (b) Write out the results of the "subgroup fill" part of step 3 (i = 3). That is, for all t corresponding to the elements of H3, write out the formula for y(t) in terms of the inputs x (the output of step 2, i = 2). (c) Draw the corresponding subgroup subdiagram for step 3 (i = 3).
Expert Answer:
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
Students also viewed these mathematics questions
-
CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...
-
"internet radios" for streaming audio, and personal video recorders and players. Describe design and evaluation processes that could be used by a start-up company to improve the usability of such...
-
Consider the generalized externality problem. Assume the damage and cost functions are given by: (a) Determine the non-regulated level of E if the polluter has the right to pollute. (b) Determine the...
-
Complete the details in the proof of the multinomial theorem. Multinomial theorem. For positive integers n, t, the coefficient of x1n1x2n2x3n3 . . . xtnt in the expansion of (x1 + x2 + x3 + . . . +...
-
In Exercises use the definition of infinite limits to prove the statement. 1 lim x3+ x - 3 =
-
Should the requirements of the UCC be subject to the application of reliance theories? Go back and review the facts in Case 21-3 about the coal contract. Should silence followed by contract execution...
-
Laminar flow in a triangular duct (Figure 3B.2) 2 one type of compact heat exchanger is shown in Figure 3B.2 (a). In order to analyze the performance of such an apparatus, it is necessary to...
-
At the conclusion of a second-year practical session, two groups of students engage in a heated debate. Group A students are certain that their results (Table 1) are statistically comparable to those...
-
Irwin, Inc. constructed a machine at a total cost of $25 million. Construction was completed at the end of 2017 and the machine was placed in service at the beginning of 2018. The machine was being...
-
For a project manager working in the federal government, creating an Independent Government Cost Estimate (IGCE) is crucial to defining and developing successful acquisitions. What is the primary...
-
Best Poor Man's Country and Revolution What were the opportunities for individuals in this time period, share with the class the insights that you perceived about Pennsylvania? Did everyone have an...
-
You are right about any policy starting up needing a funding source. Determining where that funding will come from can be the hard part. It is important to map out a budget for the policy and promote...
-
What characteristics of a commonweal organization would likely conflict with the culture of a typical business organization that contracts to provide a public service?
-
1. Why did Mexicans volunteer for service during World War II? 2. What role did Mexican women play in the home front during the war? 3. What impact did urban living have on Mexicans? 4. Who were the...
-
A 10-5 is performed on a culture of bacteria in order to perform viable plate counts. From the dilution, *0.1 mL* of solution is plated on solid media, and 35 colonies of bacteria grow on the plate....
-
Is it a breach of fiduciary duty for a director of a real estate investment trust (REIT) negotiating a joint venture on behalf of the REIT with another director for the development of a portfolio of...
-
Consider an open economy characterized by the following equations: The parameters \(m_{1}\) and \(x_{1}\) are the propensities to import and export. Assume that the real exchange rate is fixed at a...
-
Consider an open economy in which the real exchange rate is fixed and equal to one. Consumption, investment, government spending, and taxes are given by where \(Y^{*}\) denotes foreign output. a....
-
Label each of the following statements true, false, or uncertain. Explain briefly. a. The interest rate parity condition means that interest rates are equal across countries. b. Other things being...
Study smarter with the SolutionInn App