Question: Show that if C is a code with a generator matrix, then (C ) = C.

Show that if C is a code with a generator matrix, then (C⊥)⊥ = C.

Step by Step Solution

★★★★★

3.34 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

We need only show that C and C ... View full answer

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

Document Format (2 attachments)

PDF file Icon

1623_606b0df173b72_699468.pdf

180 KBs PDF File

Word file Icon

1623_606b0df173b72_699468.docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Show that if C is represented by r(t) with arbitrary parameter t, then assuming k > 0 asbefore. (23***) T(1) (r' r')(r" r") (r' r")

Q:

Show that if C is a condition that elements of the n-ary relations R and S may satisfy, then sC(R S) = sC(R) sC(S).

Q:

Show that if C = 2, the statistic Q defined by Eq. (10.3.4) can be rewritten in the form il

Q:

2 . 7 . 9 In each part, a parity - check matrix for a linear code C is given. Find ( i ) a generator matrix for ; ( ii ) a generator matrix for C . * ( c ) H = [ 1 1 1 1 1 0 1 0 1 0 1 1 1 0 0 0 1 0 0...

Q:

Problem 1 . 1 . ( 7 , 4 ) block code has the generator matrix G: G = | ? ? [ 1 , 0 , 0 , 0 , 1 , 0 , 1 ] , [ 0 , 1 , 0 , 0 , 1 , 1 , 1 ] , [ 0 , 0 , 1 , 0 , 1 , 1 , 0 ] , [ 0 , 0 , 0 , 1 , 0 , 1 , 1...

Q:

Q3. [12M] For the (7,4) code with the generator matrix given by G. Find: (A) Probability of undetected codeword error over the BSC with crossover 1 0 0 1 0 01 1 010 0 0 0 1 101 100 0100 probability...

Q:

6. (10 points) If a (7,4) linear block code has a generator matrix [1 0 0 0 1 1 0] 0 1 0 0 0 1 1 G= 0 0 1 0 1 1 1 0 0 0 1 1 Find the corresponding code word c for the message m= [1 0 0 1]

Q:

This is numerical analysis 1. Construct an efcient routine for solving linear systems. Let 10 7 0 2 4 2 4 U = O 2 6 , A = 4 9 3 , b = 8 2 1 7 6 0 0 5 (a) Create two routines for an n x n matrix, one...

Q:

Let C be the ternary 6 , 4 - code with generator matrix given by G = [ 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 ] Which of the following sets are information sets for C ? S 1 = { c o l 1 , C o...

Q:

Exercise 1.2 Let W be an rs random matrix, and let A and C be nr and ns matrices of constants, respectively. Show that E(AW +C) = AE(W)+C. If B is an st matrix of constants, show that E(AWB) =...

Q:

A loan of 1,000 must be repaid by making annual payments of 100 beginning at the end of the fifth year and continuing for as long as necessary thereafter. The effective discount rate is 5%. Find the...

Q:

Asked you to write a mechanism describing formation of benzaldehyde diethyl acetal from benzaldehyde and ethanol, write a stepwise mechanism for the acid hydrolysis of this acetal.

Q:

14.41 CHALLENGE Use high school grades and SAT scores to predict high grade point averages. Run a logistic regression to predict HIGPA using the three high school grade summaries and the two SAT...

Q:

6. What is Grandmas rule, and how does it relate to the Premack principle?

Q:

If we assume that all boys have no sperm cells at age 11 (11.0 years) and all have sperm cells at age 18, then estimate the probability of first developing sperm cells at ages 12 (i.e., between 12.0...

Q:

Provide a stem-and-leaf plot of the age at first sperm-positive urine specimen? Pediatrics, Endocrinology A study was performed among 40 boys in a school in Edinburgh to look at the presence of...

Q:

What will be the revised sample size estimate in Problem 10.44 if the lack of compliance is taken into account? Investigators expect that not all participants will comply. In particular, they project...

Q:

Please help me to solve it, just an answer will make sense, thank you! Question 5 4 pts Look at the test output shown below, After considering the results of this test, how would you proceed to test...

Q:

Show all steps. Beta and CAPM Suppose the risk-free rate is 4.7 percent and the market portfolio has an expected return of 11.2 percent. The market portfolio has a variance of .0382. Portfolio Z has...

Q:

According to the residual theory of dividends, if the firm's equity need is less than the amount of retained earnings, the firm would Answer borrow to pay the cash dividend. declare a dividend equal...