how 2 get gf

  1. start w/ the integers Z
  2. take a prime p(has 2 be prime)
  3. set p equal to 0 (take equivalence classes of addititon by pZ if u want)
  4. now u have GF(p)
  5. (optional) take a power n
  6. find a polynomial w/ no factors (about 1/n of 'em are, basically same as prime tbh)
  7. take all the polynomials over GF(p)
  8. set that polynomial equal to 0
  9. now u have GF(p^n)
  10. use ur gf to make vector spaces and shit
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