Anzahl formulas of subspaces in symplectic spaces and their applications (Q1947093)

Let \(\mathbb F_q^{2\nu}\) be the \(2\nu\)-dimensional symplectic space over the finite field \(\mathbb F_q\). In this paper, the authors focus on the computation of \(N(i;m,s;m_1,s_1;2\nu)\), the size of a family of special subspaces in \(\mathbb F_q^{2\nu}\), and discuss its applications to the constructions of Cartesian authentication codes, pooling designs and strongly regularized semilattices, respectively.