Construction
Traditionally, an AG-code is constructed from a non-singular projective curve X over a finite field by using a number of fixed distinct -rational points
- := {P1, P2, ..., Pn} ⊂ X ( ) on X.
Let G be a divisor on X, with a support that consists of only rational points and that is disjoint from the 's. Thus ∩ supp(G) = Ø
By the Riemann-Roch theorem, there is a unique finite-dimensional vector space, with respect to the divisor G. The vector space is a subspace of the function field of X.
There are two main types of AG-codes that can be constructed using the above information.
Read more about this topic: Goppa Code
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