Help in a channel coding question

[blue_tiger30]

Homework Statement

Consider a particular channel coder that has a generator matrix G =[1 1 1 1 1]
1 -Generate all the allowable codewords for c . What do you think this code is called?
2- What is the minimum distance for this codeword? Describe how it might work to correct errors.

Homework Equations

c=m*G = [m*p m*I]

The Attempt at a Solution

I know the 1st part for the question which is 2 allowable codewords 00000 , 11111 . but i tried looking for what these codes are called I couldn't find a name for them ! or is he meaning the name of the channel coder ?
the 2nd part I got the minimum distance to be 5 since that we only have 2 allowable code and the change in them is 5 , I don't know how to describe how they might correct an error so if u could please help me in this part as well .

Please notify me if u think my answers are wrong as well

many thanks

 

[nilesh_pat]

For part 1, the code is called a repetition code. It is a type of error-correcting code in which the same bit (generally a binary digit) is sent multiple times to increase the probability that the receiver will correctly receive the data.For part 2, the minimum distance for this codeword is 5. This means that any two codewords must differ in at least 5 bits in order for the code to be able to correct any errors. The way this code works to correct errors is by having the receiver compare the received codeword with all the possible codewords and then choose the one that is the closest match. If the received codeword differs from the closest codeword by more than the minimum distance, then an error is assumed to have occurred. In this case, the receiver can then send a request for a re-transmission of the codeword.