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Math Help - Reed Solomon & Galios

  1. #1
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    Reed Solomon & Galios

    Hi All:

    I hate to admit I'm stuck, but I'm stuck. I am trying to find out how Reed Solomon error correction works but I'm stuck in the jargon. If I ever knew what a Galios field was it has been forgotten for thirty years. Could someone explain some terms such as "Primitive" Better still, just a general outline of how the flipping thing works in English.

    Thanks
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  2. #2
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    Quote Originally Posted by exweedfarmer View Post
    Hi If I ever knew what a Galios field was it has been forgotten for thirty years.
    30 years! Wow that is like twice as old as Galois.
    But anyways a Galois Field is a finite field.
    I guess they are named after him for he was the first to rigorously study them. Same reason why we do not say a commutative group rather we say Abelian group.
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    30 years! Wow that is like twice as old as Galois.
    But anyways a Galois Field is a finite field.
    I guess they are named after him for he was the first to rigorously study them. Same reason why we do not say a commutative group rather we say Abelian group.
    Not quite. He got himself killed in a duel at the age of 20. He was making me feel real stupid until I read that. I could still use the definitions of "Primitive" and "Syndrome" as related to finite fields.
    I've had some conficting data in my research.
    P(x)= x^8+x^4+x^3+x^2 +1 Now in this case, do the plus signs mean add or XOR or AND? Like I said. I'm lost in jargon.
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  4. #4
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    Quote Originally Posted by exweedfarmer View Post
    Not quite. He got himself killed in a duel at the age of 20.
    That is one of my favorite math stories. I love to sit back on a chair and think.... if only he lived a natural life.... maybe Gauss would not have been Gauss. See Gauss lived a full life (78). So he had much time to do math. Galois only had a few years. But I think it is pretty fair match Galois solved insolvability problem at 19 that got the best mathematicians and Gauss solved quadradic reciprociy which also got mathematicians. So I do not know who would have been better.
    I also like to think of Riemann the same way, he lived half as long as Gauss. Maybe he would have caught up and been almost as good as him, that is what some math historians think.
    (Of course, I, in a few years, I will put these two men into shame.)
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