Goppa Codes - Department of Mathematics
Goppa Codes - Department of Mathematics
Goppa Codes - Department of Mathematics
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
<strong>Goppa</strong> <strong>Codes</strong> Key One Chung<br />
✬<br />
Definition. Let C be a curve defined over Fq and let f := g/h ∈ Fq(C). The<br />
divisor <strong>of</strong> f is defined to be div(f) := � P − � Q, where � P is the<br />
intersection divisor C � Cg and � Q the intersection divisor C � Ch.<br />
Note that since deg(C � Cg) = deg(C � Ch), we have deg div(f) = 0.<br />
Definition. Let D be a divisor on the nonsingular projective plane curve C<br />
defined over the field Fq. Then the space <strong>of</strong> rational functions associated to D is<br />
✫<br />
L(D) := {f ∈ Fq(C)|div(f) + D ≥ 0} � {0}.<br />
Note L(D) is a finite dimensional vector space over Fq.<br />
✩<br />
✪<br />
Page 26
Change language