Sections of the Del Pezzo surfaces and generalized weights
Let \(C\) be an \([n,k;q]\) code that is a linear code of length \(n\) and dimension \(k\) over \(GF(q)\). For any subcode \(D\) of \(C\), let \(\chi (D)\) be the support of \(D\), i.e. the set of positions where not all the codewords of \(D\) are zero. Further, let \(w_S\) \((D):=|\chi(D)|\) be the support weight of \(D\). For \(1\leq r\leq k\), the \(r\)-th generalized Hamming weight of \(C\) is defined by \(d_r=d_r(C)= \min \{w_S(D)\mid D\) is an \([n,r;q]\) subcode of \(C\}\). The sequence \((d_1,d_2, \dots, d_k)\) is the weight hierarchy of \(C\). In this paper the author analyzes sections of split Del Pezzo surfaces and computes the weight hierarchy for algebraic-geometric codes constructed from Del Pezzo surfaces.
scientific article; zbMATH DE number 1253949