Question: 1. Show that if g(X) generates a cyclic code of odd minimum distance d, then (X+1)g(X) generates a cyclic code of minimum distance at

1. Show that if g(X) generates a cyclic code of odd minimum

1. Show that if g(X) generates a cyclic code of odd minimum distance d, then (X+1)g(X) generates a cyclic code of minimum distance at least d+1. 2. The polynomial g(X)=1+X+X3 generates a cyclic Hamming code of length 7. Find its dimension and minimum distance. 3. Find the dimension and minimum distance of the code of length 7 generated by the polynomial (X + 1)g(X) where g(X)=1+X+X.

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 Programming Questions!

A firm needs to purchase an office equipment for its new project. The total cost of the equipment is $1,000,000. By increasing employee productivity with this equipment, it is estimated that the firm...

Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...

Q1. You have identified a market opportunity for home media players that would cater for older members of the population. Many older people have difficulty in understanding the operating principles...

Problem 5.y 1. Show that if g(X) generates a cyclic code of odd minimum distance d, then X 1)g(X) generates a cyclic code of minimum distance at least d+1. enerates a cyclic Hamming code of len 7....

seventh pages Chapter 3 Curve Sketching How much metal would be required to make a 400-mL soup can? What is the least amount of cardboard needed to build a box that holds 3000 cm3 of cereal? The...

3 ,,uoh "gram 3 Eww 3 m T mm H a 3 .2 ' m w .,.m.av>v 3. m. @3on we geonwoaoa mm H "with M'nr H E. wads + we A at. ES 0 3.8V WEE 3563 mo wow 23 E m \"9H .3 avgmeMm\" mnemagouom Aggy\"...

Let r and s be solutions to the quadratic equation x 2 b x + c = 0. For n N, define d0 = 0 d1 = r s dn = b dn1 c dn2 (n 2) Prove that dn = r n s n for all n N. [4 marks] (b) Recall that a commutative...

Math\t107-6381\t-\tQuiz\t#4\t-\tSchultz\t-\tDue\tFebruary\t21,\t2016\t-\tpage\t1\tof 3 Follow\tthese\tdirections\tcarefully. This\tquiz\tis\tdue\tby\t11:59\tEastern\ttime\ton\tFebruary\t21,\t2016. o...

Describe how to construct the function cpo ((D E), v) of two cpos (D, vD) and (E, vE). Prove that ((D E), v) is a cpo. (You may use facts about least upper bounds provided you state them clearly.)...

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

Lee's Machine shop has estimated net requirements for a particular part as follows: Period Net requirement 1 2 3 4 5 6 18 19 150 20 30 40 140 150 150 150 150 10 80 Ordering cost associated with this...

Two predictors of infant mortality seem to be significant. If you could find a way to use both of them as predictors simultaneously, what do you think you would find?

an AICPA member in public practice must meet certain general standards unde 1.300.001 the general standard rule

Suppose a stock price follows the Ito process dS = aS dt + bS dB, (1) where a, b, , are all constants non-zero constants, and , 6= 0, 1. Find F(S), a differentiable function of the stock price,...

Miss Wells has purchased the shares of two companies over the years. Each company has only one class of shares. Purchases and sales of shares in the first of these companies, Memo Inc., are as...

Hager Company sold some of its plant assets during 2016. The original cost of the plant assets was $750,000 and the accumulated depreciation at date of sale was $700,000. The proceeds from the sale...

rn Complete the table below for the missing amounts. |(Click the icon to view the table.) Compute the missing information, starting with scenario A, then for scenarios B and C. A Number of units...

Can we put that she will be making weekly payroll deductions inthe amount of $52.75 to the housing equalling $211.00 monthly

Sketch the conic sections whose polar coordinate equations are given. Give polar coordinates for the vertices and, in the case of ellipses, for the centers as well. r || 8 2 + cos 0

Find dy/dx. y = T/4 tanx eVt dt

To illustrate that the length of a smooth space curve does not depend on the parametrization you use to compute it, calculate the length of one turn of the helix in Example 1 with the following...

A discount furniture store bought a waterbed at the wholesale price of $665. The regular price of the waterbed is set so that, in a 20% off sale, the rate of markup on selling price is 30%. a. What...

Fashion Master purchased mens sweaters for $72 less 40% and 15%. The normal rate of markup on selling price is 40%, and overhead is 25% of the regular selling price. The sweaters were reduced to...

Calculate the missing values