Goppa Codes - Department of Mathematics

Goppa Codes Key One Chung
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Definition. • Let C be a curve defined by over Fq. A divisor D on C over Fq
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is an element of the free abelian group on the set of points(of arbitrary
degree) on C over Fq.
Thus every divisor is of the form D = � nQQ, where the nQ are integers
and each Q is a point (of arbitrary degree) on C.
• If nQ ≥ 0 for all Q, we call D effective and write D ≥ 0.
• We define the degree of the divisor D = � nQQ to be
deg D = � nQdeg Q.
• the support of the divisor D = � nQQ is supp D = {Q|nQ �= 0}.
Note C � C ′ is an effective divisor of degree de.
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