Question: Suppose C is a linear code over GF ( qm ) , m ~ 2 . Let S be the set of codewords such that

Suppose C is a linear code over GF(qm), m ~ 2. Let S be the set of codewords such that all components of these codewords are in GF(q). Show that S is also a linear code over GF(q). Is S a linear code over GF(qm)?

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!

Q:

Mathematics Coding Theory Problem. Z_2 = {0,1} and code length of 8 PROBLEM 2. Let C C Z have the generator matrix 0 0 0 0 0110 1 0 0 01 0 0 10 00110 G = 00100101 0 0001010 1 0 0 0 0110 The code C...

Q:

Let C be the set of all 4 x 4 matrices over F2 with even number of ones in every row and every column, for instance 1001 0011 1 0 1 1 1 1 0 1 is such a matrix. View C as a subset of F6. Part 1. (10...

Q:

Portray in words what transforms you would have to make to your execution to some degree (a) to accomplish this and remark on the benefits and detriments of this thought.You are approached to compose...

Q:

A creative engineer suggests structuring the TLB so that not all the bits of the presented address need match to result in a hit. Suggest how this might be achieved, and what might be the costs and...

Q:

Here is the new homework question. Please review the General Homework instructions due to the instructor being so strict. Were there any podcasts or Homework document notes that you needed me to...

Q:

Suppose that R(A, B, C) is a relational schema with functional dependencies F = {A, B C, C B}. (i) Is this schema in 3NF? Explain. [2 marks] (ii) Is this schema in BCNF? Explain. [2 marks] (b)...

Q:

Prolog You are approached to compose a Prolog program to work with twofold trees. Your code shouldn't depend on any library predicates and you ought to expect that the mediator is running without...

Q:

My tutor that I Have been using for the past 5 weeks bailed on me with an assignment due tomorrow by 9PM Central USA time. There is 3 weeks left in this course. I am looking for someone that is...

Q:

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

Q:

A discrete sequence {xn} can be converted into a continuous representation x(t) = ts X n= (t n ts) xn, where ts is the sampling period. (a) State two characteristic properties of Dirac's function. [2...

Q:

1. Consider that n subjects give data, (y, X1X12),..., (ynxnxn2), which are statistically independent and satisfy the model Yi = Bo + B(Xi x ) +Bz (Xzi Xz)+& - ,i=1,n where x and x are non-random;...

Q:

Kamal purchased a new rental property on 3 July 2018 and immediately rented it out earning $520 per week in rental income. He paid the following amounts in relation to the property. $ Purchase price...

Q:

Which of the following is an agreement between two ( 2 ) or more persons to share a common interest in a commercial endeovor and to share profits and losses? Multiple Choice A sole propinetorship A...

Q:

How does non verbal communication and emotions impaction negotiations