The next 2 videos of this series can not come soon enough! I'm in my last year of my PhD and I have just started to delve into this stuff, and your videos are easily, by and far, the BEST resources I can find on learning this stuff. Thank you!!!
You're killing me here. where's the rest? This is easily the best explanation I saw and you're cutting us off right when we got to the good stuff (RS).
I'll just chime in and say that your way of explaining these things is really good, and you manage to always find a different way to explain it than everyone else. No pressure, but I would love to see a 3c
Thanks. Part of me wants to finish this series, but I also have to admit I've lost the drive to make them. I hope you can find the information somewhere else online.
@@eigenchrisplease dont abandon this series if possible your contents have been very resourceful and we are extremely grateful for your time and effort
I'm currently working on SFEC Hamming Encode/Decode and your video is THE BEST of all resources I can find. This helps me a lot and it is crucial for me to finish the project. Thank you!!!!!
The stages involved in solving problems related to non-binary codes in finite fields, specifically in the context of error correcting codes, include: 1. Understanding the theory of finite fields and the algebraic properties they offer for coding theory. 2. Generalizing codes like Hamming codes to correct multiple errors, such as with BCH codes. 3. Exploring different types of error correcting codes like Reed-Solomon, Bose-Chaudhuri-Hocquengham, and Goppa codes. 4. Developing basic facts about finite fields and linear algebra over them to construct and efficiently encode/decode error correcting codes. 5. Utilizing techniques like maximum distance separable (MDS) codes and maximum likelihood decoding for optimal performance in finite-length codes and erasure channels.
This is the BEST! What a pity, there is no further lecture. I have learned how RS code works from other resources, but still do not know how it is related to "prime", "cyclic", and "linear", and why "MDS". Almost there, but it came to an abrupt end. 😭
Anyone knows bibliography about the manipulation of polynomious with symbols? I need to understand reed solomon decoding, but i don't know how the symbols need to be use or operate
But GF(4) = GF(2^2), GF(8) = GF(2^3) etc can be fields if defined with polynomial arithmetic so that division work again and every member has a multiplicative inverse, correct? e.g. GF(256) is used for AES as a field.
It wasn't supposed to be... I fell off making this series because it wasn't as popular and the tensors/relativity videos were much more popular. I have some notes for the EEC4 videos here, but they are a bit disorganized: github.com/eigenchris/MathNotes
@@eigenchris These are VERY much appreciated though. You have a simple, straightforward style to demonstrating these, I'm using them to implement things in python for my own learning. For example I had made my own matrix class, and I was able to use that to generate generator and check matrices for a hamming code, apply them to a message, and get [0 0 0] out. FeelsGoodMan. I also realised from your video and 3blue1brown's (which mostly avoids matrices) that simply reorganising the generator matrix gets you the 'message first' vs the 'power of two' message-in-code ordering (non-systemic vs systemic?). There is really not much on youtube getting into more advanced ECCs (past hamming...) that is so easy to take in and learn from. Thanks so much, I hope you are someday able to make a video on checking and correcting in cyclic codes.
The next 2 videos of this series can not come soon enough! I'm in my last year of my PhD and I have just started to delve into this stuff, and your videos are easily, by and far, the BEST resources I can find on learning this stuff. Thank you!!!
Oh man can you make video about your field of study, I would glad to see it
You're killing me here. where's the rest? This is easily the best explanation I saw and you're cutting us off right when we got to the good stuff (RS).
These videos were so good for helping me understand wish the series had continued
I'll just chime in and say that your way of explaining these things is really good, and you manage to always find a different way to explain it than everyone else. No pressure, but I would love to see a 3c
Thanks. Part of me wants to finish this series, but I also have to admit I've lost the drive to make them. I hope you can find the information somewhere else online.
@@eigenchris of course. It's important that making such projects is fun
@@eigenchrisplease dont abandon this series if possible
your contents have been very resourceful and we are extremely grateful for your time and effort
I'm currently working on SFEC Hamming Encode/Decode and your video is THE BEST of all resources I can find. This helps me a lot and it is crucial for me to finish the project. Thank you!!!!!
Nice playlist, looking forward to the voyager error codes, thank you!
The stages involved in solving problems related to non-binary codes in finite fields, specifically in the context of error correcting codes, include:
1. Understanding the theory of finite fields and the algebraic properties they offer for coding theory.
2. Generalizing codes like Hamming codes to correct multiple errors, such as with BCH codes.
3. Exploring different types of error correcting codes like Reed-Solomon, Bose-Chaudhuri-Hocquengham, and Goppa codes.
4. Developing basic facts about finite fields and linear algebra over them to construct and efficiently encode/decode error correcting codes.
5. Utilizing techniques like maximum distance separable (MDS) codes and maximum likelihood decoding for optimal performance in finite-length codes and erasure channels.
God bless you !! One of the best videos ever on these less-explained things !!
Great videos, I hope that one day you continue this series.
This is the BEST!
What a pity, there is no further lecture.
I have learned how RS code works from other resources, but still do not know how it is related to "prime", "cyclic", and "linear", and why "MDS".
Almost there, but it came to an abrupt end. 😭
Your explanations are great! Please continue the series.
Soooo, what happened to the next videos in the series? Uploaded June 2021, and it's the last in the playlist :(
Thanks so much for doing these. I cannot wait for the next in this series.
So nice, please add the rest of series.
Amazing series. Looking forward to the next video!
I think you may want to clarify at the end that fields of order p^n (n >= 2), although they exist, are not Z_(p^n).
P. S. there's a typo at 9:21
I'm going to explain that in the next video. And yeah, that's a typo. But it's a minor enough one that I'm probably just going to leave it in.
@@eigenchris looking forward to your next video.
Excellent lecture series. More please, sir!
Noooooooooo, there's no contijuation video?!?!? 🙈🙈🙈 anyhow, great work!!! Looking forward to the continuation! 🖒
Sir, you are a work of God !
loving this videos! keep them going
Anyone knows bibliography about the manipulation of polynomious with symbols? I need to understand reed solomon decoding, but i don't know how the symbols need to be use or operate
Please post 3c. Looking forward to 4b.
Next video link plz... Full playlist have only 7 videos?? Or more...
hope finish this series in 2021
But GF(4) = GF(2^2), GF(8) = GF(2^3) etc can be fields if defined with polynomial arithmetic so that division work again and every member has a multiplicative inverse, correct? e.g. GF(256) is used for AES as a field.
Yes. There's a finite field for any prime power that is constructed with polynomials.
Can you do a video on encoding and decoding Ternary codes e.g. Golay Code?
Is this the las video in this series?
It wasn't supposed to be... I fell off making this series because it wasn't as popular and the tensors/relativity videos were much more popular. I have some notes for the EEC4 videos here, but they are a bit disorganized: github.com/eigenchris/MathNotes
@@eigenchris What a pity. This is the BEST one I ever met!
@@eigenchris These are VERY much appreciated though. You have a simple, straightforward style to demonstrating these, I'm using them to implement things in python for my own learning. For example I had made my own matrix class, and I was able to use that to generate generator and check matrices for a hamming code, apply them to a message, and get [0 0 0] out. FeelsGoodMan. I also realised from your video and 3blue1brown's (which mostly avoids matrices) that simply reorganising the generator matrix gets you the 'message first' vs the 'power of two' message-in-code ordering (non-systemic vs systemic?). There is really not much on youtube getting into more advanced ECCs (past hamming...) that is so easy to take in and learn from. Thanks so much, I hope you are someday able to make a video on checking and correcting in cyclic codes.
great video! very helpful.
Hey, was there never a 3c video how to correct using cyclic polynomial codes?
I'll try to get that one out later this year.
@@eigenchris Thanks for the update! Looking forward to it.
where can i find your next video on prime powers
It doesn't exist yet... the best I can give you is this link to my rough notes on ECC4: github.com/eigenchris/MathNotes
Fabulous!
great video!
Oh god finally
Feild! 15:35
I'm not an English major and therefore I make no guarantees about the accuracy of my spelling.
ADD MOREEEEE PLZZ
waiting for 4b😭
Its not cyclic is cyclic.
Hehe enby codes
Don't stop me now 🥲
excellent video!