This series of lecture is truly outstanding. I very much appreciate the amount of patience the professor has and his frequent repetition of concepts to reinforce the main ideas. That said, I don't think anyone watching these lectures should think this topic is easy or easy to learn. It takes hard work and patience to understand Cyclic, BCH and Reed Solomon codes. The quality and down to earth approach of these lecture simply minimizes the time that you'll spend being confused.
consider the map x→x^p. This is in fact an endomorphism of Galois field F_q and is an identity map when restricted to F_p. This make \beta and \beta^p had the same minimal polynomial.
The t=4 case doesn't make much sense based on the result that k=1. If we are only sending one information bit at most 1 error can happen we care about.
With error correction, you focus on correcting the entire word. Not the message only, since an error could affect any part of the codeword. Sometimes the error happens in the message, other times in the parity check bits. You can never know which one was affected, so you need to be able to correct the entire word at that point.
This series of lecture is truly outstanding. I very much appreciate the amount of patience the professor has and his frequent repetition of concepts to reinforce the main ideas. That said, I don't think anyone watching these lectures should think this topic is easy or easy to learn. It takes hard work and patience to understand Cyclic, BCH and Reed Solomon codes. The quality and down to earth approach of these lecture simply minimizes the time that you'll spend being confused.
Awesome 👏
Thank you sir for these videos.
How do we arrive at p(z) ?
I am not getting the point how all z terms are cancelled and getting minimal polynomial in x terms only ???
All additions are Modulo-2 additions where 1+1 = 0.
what is the logic behind these,
1,2,4,8....
3,6,9,12...
5,10...
7,11,13,14...
How to choose what terms will form the minimal polynomial?
consider the map x→x^p. This is in fact an endomorphism of Galois field F_q and is an identity map when restricted to F_p. This make \beta and \beta^p had the same minimal polynomial.
👍
you are writting all the book thing nothing else to understand
The t=4 case doesn't make much sense based on the result that k=1. If we are only sending one information bit at most 1 error can happen we care about.
With error correction, you focus on correcting the entire word. Not the message only, since an error could affect any part of the codeword. Sometimes the error happens in the message, other times in the parity check bits. You can never know which one was affected, so you need to be able to correct the entire word at that point.