The [n, 1, n]-binary repetition code has the messages 0 and 1, and the codewords 00...0and 11 1 each of length n.Find a generator matrix and a parity check matrix for this code.

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Answered: The [n, 1, n]-binary repetition code…

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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In cryptography often use matrix operations but modulo some M for the calculations (for example, in Hill substitution ciphers.) Do the following mod 26 calculations (see the attached multiplication table mod 26): a. Compute the following matrix product modulo 26 [17 22 29 41 [21 1 1125 18 22 20 46 13 17 24 19]
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
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† 3.2. Let C be the binary linear code with generator matrix 1 0 0 1 1 01 G= 0 1 0 1 0 1 LO 0 1 1 1 0 List all the codewords in C and find the weight of each codeword. What is her d(C)?
Executing the following sage code constructs a matrix Q, then prints the matrix and its reduced row echelon form. Q=matrix(QQ, 4, 3, [-7, -22,-4, 12, 137,-13,-18, -213,21,15,115,-5]) print(Q) print() print(Q.rref()) The output is: -4] [ -7 -22 [ 12 137 -13] [-18 -213 21] [ 15 115 -5] [ [ [ 1 0 0 0 6/5] 1 -1/5] 0 0 0] 0] Are the columns of matrix Q linearly dependent, or linearly independent?
6.) Find the rank of the matrix A 2031 0211 32 11 5453

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The [n, 1, n]-binary repetition code has the messages 0 and 1, and the codewords 00...0 and 11 1 each of length n. Find a generator matrix and a parity check matrix for this code.