6. Polynomials a) Generate the elements of the field GF(24) using the irreducible polynomial f(x)= x²+ x³+1 b)(6pt) Using the above results, calculate (x3+x2+1)* (x²+1) c) (6pt) Calculate (-x²+x)-1 d)(6pt) Calculate (x+1)/(x³-1)
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- List the restrictions to arrayQ1 2(a). Show how the AND-OR array should be programmed to implement the SOP expressions. Y3 АВС+ AВС + АВС A A B В сTo generate linearly spaced vector of 12 linearly spaced numbers from 6 to 48 * linspace(12,6,48) linspace(48,12,6) O linspace(6,12,48) linspace(6,48,12)
- Python application creation The system call inv in the numpy.linalg library can be used to calculate the inverse of a matrix. A basic 2 by 2 matrix's inverse can be calculated using Python code. The identity matrix I is then generated by multiplying the inverse of A by itself for proof.(1 0 0 0 1 1) For a given code C, the generator matrix is G = (0 1 1 \o 0 1 1 1 0 a) Find all the codewords of this code C. b) Construct the standard array for C. c) Decode 111111.Let S = {1, 2, 3, 4, 5} a) List all the 3-permutations of S.b) List all the 3-combinations of S
- Write a phyton program that solves the following given problems: 1. Perform Matrix Inversion for matrix [A] and [B]Define, A = Find x. Hint: use numpy.linalg.inv and the @operator for matrix multiplication. 3 6 2 b = 10 5 2 1 7 5 Y = 3 Ax + b = Y N[] [] dir_euler Write a function "dir_euler(digraph)" that takes in a connected, directed graph as its input, and then determines whether or not a directed Eulerian circuit exists. After compiling the above cell, you should be able to compile the following cell and obtain the desired outputs. print(dir_euler({"A" : ["A", "B", "C"], "B" : ["A"], "C" : ["A"]}), dir_euler({"A" : ["B", "D"], "B" : ["A", "D"], "C" : This should return True False ["C", "D"], "D" : []})) Python Python