RC4 has a secret internal state which is a permutation of all the possible values of the vector S and the two indices i and j a. Using a straightforward scheme to store the internal state, how many bits are used? b. Suppose we think of it from the point of view of how much information is represented by the state. In that case, we need to determine how may different states there are, then take the log to the base 2 to find out how many bits of information this represents. Using this approach, how many bits would be needed to represent the state?

We are given a code symmetry, that takes an n x n matrix as its argument. It returns true if the matrix is symmetric and false if it is not. The run time of the code is calculated by counting how many times the /= comparison is executed.  procedure symmetry(M)      for x:=1 to (n-1)            for y:=(i+1) to n               if mxy /= myx then return false               else return true (a) Calculate the best case run time for symmetry (will be a number). (b) Calculate the worst case run time for symmetry (will be a polynomial in n, it will be helpful to draw matrices of different sizes and compare the number of comparisons to find a pattern).  (c) Determine the worst case run time in big O notation (d) Using the following definition of big O notation, prove the answer to (c) Definition: Let f and g be functions from the set of integers or the set of real numbers to the set of real numbers. We say that f(x) is O(g(x)) if there are constants C and k such that whenever x > k. [This is…

Construct a (6, 3) binary linear code with generator matrix 1 0 0 11 0 G=0 10 0 1 1 [o 0 1 1 0 1, Decode each of the received words 001001, 011000, 000110, 100001 by the following methods: a. Nearest-neighbor method. b. Parity-check matrix method. c. Coset decoding using a standard array. d. Coset decoding using the syndrome method.

Write MATLAB code. For input vector x, write a function to return vector y in which all the elements in vector x are duplicated. Example: If input x = [1 0 4], then y = [1 1 0 0 4 4].