Question: Let g be a k x n matrix whose first row is gOgl' gn-kOO .. 0 where g(x) = go + glX + ... +

Let g be a k x n matrix whose first row is gOgl'" gn-kOO .. ·0 where

g(x) = go + glX + ... + gn_kxn-k is a polynomial of degree n - k with

go =J O. The remaining k - 1 rows are the first k - 1 cyclic shifts of this row. Let G' be the matrix constructed in the same way from grev. Show that G and G' generate equivalent codes.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Systems Analysis Design Questions!

Problem #1: Find the values of a, b, and so that det(A) = ax? + bx +c. x -2 0 A=1|-2 x 2 3 -6 -4 Problem #1: : separate your answers with a comma | Just Save ' | Submit Problem #1 for Grading Problem...

MATH 3210 Practice Final Exam for Discrete I You now have several quizzes and hour exams to study. The following in mainly a repetition of your previous practice and actual exams. 1. (a) Use truth...

1. Let A = 1 O O 0 (a) Calculate det(A). Briefly explain why A is invertible. (b) Find A-1. (c) Solve the matrix equation Ax = b if X= and b = -4 Z2. Imagine a 2-player board game consisting of a...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

# 5: Fourier Interpolant and DFT 1 The Discrete Fourier Transform (DFT) of a periodic array fj , for j = 0, 1, . . . , N 1 (corresponding to data at equally spaced points, starting at the left end...

Least Squares Approximation Hector D. Ceniceros 1 Least Squares Approximation Let f be a continuous function on [a, b]. We would like to find the best approximation to f by a polynomial of degree at...

If the customer agreement had precluded only class litigation and mandated class arbitration, would the court have considered the provision unconscionable? Why or why not?

In your opinion, are the other dimensions of diversity likely to have a greater or a lesser impact than the basic dimensions? Explain your answer.

9.19 A random sample of 25 tablets of buffered aspirin contains, on average, 325.05 mg of aspirin per tablet, with a standard deviation of 0.5 mg. Find the 95% tolerance limits that will contain 90%...

Air (1 atm and 30C) flows crosswise over a bare copper tube (1-in, BWG 16). The approach velocity of the air is 20 m/s. Water enters the tube at 140C and leaves the tube at an average temperature of...

A team of developers is considering including "warehouse" as an entity in its data model. The company for whom they are developing the system has just one warehouse location. Should "warehouse" be...

What are metadata? Why are they important to system developers?

Draw data models for the following entities: Movie (title, producer, length, director, genre) Ticket (price, adult or child, show-time, movie) Patron (name, adult or child, age)

0.68/1 Zeller Company estimates that 2020 sales will be $40,000 in quarter 1, $48,000 in quarter 2, and $58,000 in quarter 3, Cost of goods sold is 50% of sales. Management desires to have ending...

The following additional facts are collected for use in making adjusting entries prior to preparing financial statements for the company's first three months: a. The December 31 inventory count of...

Required information [The following information applies to the questions displayed below] Kaylee James, a connoisseur of fine chocolate, opened Kaylee's Sweets in Collegetown on February 1. The shop...