1 Introduction
2 Preliminaries
2.1 Blocking sets
2.2 Minimal codes from cutting blocking sets
3 Minimal codes from Hermitian varieties
4 On the weight distribution of minimal codes from \(\mathcal {H}_n\)
5 Minimal codes from quadrics

If n is even a nonsingular quadric \(\mathcal {Q}_n\) is projectively equivalent to a nonsingular quadric \(\mathcal {P}_n\), called parabolic, where$$\begin{aligned} \mathcal {P}_n=V_p(X_0^2 + X_1 X_2 + \cdots + X_{n1} X_n). \end{aligned}$$

If n is odd a nonsingular quadric \(\mathcal {Q}_n\) is either projectively equivalent to a nonsingular quadric \(\mathcal {E}_n\), called elliptic, or to a nonsingular quadric \(\mathcal {H}_n\), called hyperbolic, wherewith \(g(X_0,X_1)=dX_0^2+X_0X_1+X_1^2\), irreducible over \(\mathbb {F}_q\), \(d \in \mathbb {F}_q^*\), and$$\begin{aligned} \mathcal {E}_n=V_p(g(X_0,X_1) + X_2 X_3 + \cdots + X_{n1} X_n); \end{aligned}$$$$\begin{aligned} \mathcal {H}_n=V_p(X_0 X_1 + X_2 X_3 + \cdots + X_{n1} X_n). \end{aligned}$$