Reed-Solomon codes:
Given
a finite field F of order q, let n and k be chosen such that 1 \leq k
\leq n \leq q. Pick n distinct elements of F, denoted { x_1, x_2, ... ,
x_n }. Then, the codewords are obtained by evaluating every polynomial
in F[x] of degree less than k at each x_i:
C = { ( f(x_1), f(x_2), ..., f(x_n) ), f in F[x] | deg(f) < k }.
C is a [n, k, n-k+1] code. (In particular, C is MDS.)