Codes associated to the zero-schemes of sections of vector bundles (Q1046468)

The author considers algebraic geometric codes given by the image of th evaluation map \(H^0(X,L)\to\bigoplus_{i=1}^nL_{P_i}\simeq \mathbb{F}_q^n\) for a smooth projective variety \(X\) defined over \(\mathbb{F}_q\) and a line bundle \(L\). Lower bounds for the minimum distances of the codes are given by exploiting the Cayley-Bacharach property of zero-dimensional subschemes arising as zero-sections of vector bundles.