In the Shamir secret sharing scheme, we distribute a secret among q different users asfollows. If our secret a message (m₁, ..., mk) from V(k, q) then, we encode it as acodeword of the Reed-Solomon RS (9) and give one coordinate to each user. In thisproblem, we will use q = 7, k = 4 and the parity check matrix H₁ below for RS4(7).HA=11011 11 12 3 4 5 64224 11. Write a generator matrix for RS4 (7) of the form Hq-k.

To construct a Reed-Solomon code , we need to determine its parity-check matrix .Here we have to…

Answered: In the Shamir secret sharing scheme, we…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider two servers that are in a row so that the client is first served on server 1, from where the client then moves to server 2. On both servers, clients are served on a first-come, first-served basis (FIFO). Customer B arrives at the first server so that customer A is already being served there. B must therefore wait until A has been served to the end on server 1 and moves on to server 2. It is assumed that the service times of the customers on server 1 and 2 are exponentially distributed and independent, so that the average service time on server 1 is 4 ms and on server 2, respectively, 1 ms. After customer B, there will be no new customers. (Hint: Properties of the exponential distribution and the dynamics of Markov processes) a) What is the average remaining delay of customer A in the system? That is, how long does it take on average for client A to leave server 2 when client B has arrived? (Hint: Customer A's delay does not depend on customer B.) b) What is the average total…
Consider the set S1 constructed recursively. The recursive step takes a string w from S1 and concatenates the same symbol to the beginning and end of w. (1) (HD) (iv) Basis: A € 51, a € S1, and b E S1 Recursive step: if we S1, then awa E S1 and bwb E S1 Closure: S1 consists of exactly the elements that can be obtained by starting with the basis elements of S1 and applying the recursive step finitely many times to construct new elements of $1. Use induction to prove that every string in S1 is a palindrome. A palindrome is a string that reads the same from left to right and from right to left.
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11. Use the coding matrix A= O A. ACTS O B. ARMS O C. ABLE O D. ALAS 1-4 -2 and its inverse A¹ = -1 9 2 4 to decode the cryptogram -7-8 16 21
19 25 The Hill cipher with matrix 3 5 14 4 7. 11 was used to produce the following ciphertext: 1. 17 RCJCCUFYEXNUHWM Find the message.
The following is the generator matrix for a (7,4,3) Hamming code. Please encide the bits (1,1,0,0) [1 0 0 1 0 1 1 0 10 1 0 1 0 G= 0 0 1 0 0 0 0 1 1 1 1 0 0 1
The Matrix A = -529 has an eEng enualup ) = 2 A o -6 -3 -1 4- Find an ocrganunluo for this oingoncalus ニ

Let Amxn; m
Solve the following system of equations using the Gaussian algorithm with column pivoting and backward insertion: 2x2 - 4x3 + x4 = -8x1 + 2x2 + 3x3 - x4 = 3-3x1 + 2x3 + 2x4 = -32x1 + x2 - x4 = 2 Here, column pivoting means that in the respective elimination stepsu. a row swap may be carried out in the respective elimination steps, so that the elimination elementa(m)mm is the largest element of the elimination column in terms of amount.
Write the equation of the function shown below if it is known that f(0) = -18 25 20+ 15 10+ st ↓
Given the binary linear code C = {00000000, 01101111, 11011000, 11111101, 10010010, 00100101, 01001010, 10110111}. (a) Find two distinct generator matrices for C. (b) What is the dimension of C? (c) Show that the two matrices in (a) correspond to two distinct ways of encoding messages. (d) What are the three parameters n, k, and d for C?

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