All minimal [formula omitted]-codes are hyperbolic quadrics

Abstract

Minimal codes are being intensively studied in last years. [n,k]q-minimal linear codes are in bijection with strong blocking sets of size n in PG(k−1,q) and a lower bound for the size of strong blocking sets is given by (k−1)(q+1)≤n. In this note we show that all strong blocking sets of length 9 in PG(3,2) are the hyperbolic quadrics Q+(3,2).