In this question, we are going to construct a (7,3) linear block code by extending a (6, 3) linear blockcode. The generator matrix of the (6, 3) code isG =10 0 1 1 00 1 0 1 0 100101 1The (7, 3) code is extended from the (6, 3) code by appending one extra bit to into the codeword suchthat the Hamming weight of the resulting codeword is even. For example, for an input information se-quence of [111], the (6, 3) code produces an codeword of [111000] which is then extended by appendingan extra bit "1" at the end to form the final codeword of [1110001]. The reason for appending a bit "1"(instead of bit "0") is to make the Hamming weight of the resulting codeword in this example be aneven number.Another way to describe the (7, 3) code would be that it consists of a (6, 3) code with generator matrixG followed by another single parity check code with even parity.a) What is the code rate of this (7,3) code?b) What is the generator matrix of this (7, 3) code?c) What is the minimum Hamming distance of this (7,3) code?

a) The code rate of a linear block code is given by the ratio of the number of information bits to…

Answered: In this question, we are going to…

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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Solve the following problem using MATLAB. Write the syntax and the MATLAB out put on the space provided. 1. The grades of 3 students in a test are 95, 92,80 respectively; in projects are 100, 80 and 90;homework 100, 100 and 90; and in the quiz are 75;80and 90. The tests are 40% of the grade, projects 15%, homework 25%, and quizzes 20%.. Organize the data in a matrix and perform necessary operation to find the final grades of the 3 students. Use MATLAB to verify the answer. 2. An outbreak of a virus hit the local public schools. Approximately 15% of the male and female juniors and 25% of the male and female seniors are currently healthy, 35% of the male and female juniors and 30% of the male and female seniors are currently sick, and 50% of the male and female juniors and 45% of the male and female seniors are carriers of virus. There are 100 male juniors, 80 male seniors, 120 female juniors, and 100 female seniors. Using two matrices and one matrix equation, find out how many males and…
3. By hand, find all the solutions (if any) of the following linear system using the augmented matrix and Gaussian elimination (following exactly the algorithm in the notes): X1 + 2x2 + 3x3 = 4 4x1 + 5x2 + 6x3 = 10 7x1 + 8x2 + 9x3 = 14 PLEASE SHOW THE MATHLAB CODE MATHLAB CODE ARE NEED.
Cu Consider a linear code with generator matrix 0 1 G = 1 1 01 1] Encode the message 111 011 001 101 using this code. Answer: 000 -O 11
2. A transversal of an n × n matrix is a collection of n entries where no two are in the same row and no two are in the same column. How many transversals of a 5 × 5 matrix do not include any entries on the main diagonal, that is, in the (i, i) position?
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Four MBA students take the same six courses at graduate business school. Their final marks in these courses are recorded (out of 100) in the matrix M = [m] where Page 9 of 10 the final mark in course j for MBA student i ow - Coulum mij = (a) State the matrices C and Q such that (i) the entries in the product MQ are the overall average final marks for cach student and (ii) the entrics in the product CM are the overall average final marks for each course. (b) State the matrix R such that the entries in the product RM represent a 5% increase in the final grades for all students in all courses. (c) Suppose the marks in M are altered as follows: the final mark for each student in Course #2 is reduced by 3 points, the final mark for each student in Course #5 is increased by 5 points, and all other marks remain unchanged. State the matrix K so that the sum K + M has entries that reflect the alteration of the marks as described above.
Is the matrix A invertible -1 2 -6 True O False
Enter the elements of a 3 * 3 matrix using the keyboard and then find the result of summing the elements of the next diagonal as shown in the figure below ?
Do in 10mints asap
Identify the row operation that will transform the matrix 8 -9 6 1 19-50 [¹1₁ -1 4 -8 B into -1 4 -8 Type to for → and harr for .
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(2) Cryptography is the process of coding and decoding messages. One type of code that is extremely difficult to break involves using a large invertible matrix to encode a message. The receiver of the message decodes it using the inverse of the matrix. The first matrix is called the encoding matrix and its inverse is called the decoding matrix. The following example uses a 2 × 2 to illustrate the method. First we start by identifying the symbols A, B, C,..., Z with the numbers 1, ..., 26. Let a space between the words be denoted by the number 27. For example, the message "HELLO ." will be coded as 8 5 12 12 15. The basic idea is to write the message as a matrix. For example, we may write "HELLO" as the 2 × 3 matrix 8 12 15 M = 5 12 27 If we now take a 2 × 2 invertible matrix A, we may encrypt the message as AM. For example, if 3 2 A = 2) the message "HELLO." becomes "34 45, 60 72, 99 102". This message can be decoded by reversing the encoding process. PROBLEM TO BE TURNED IN: Use the…

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