Spaces of Hankel matrices over finite fields Original Research Article

Let F be a finite field. For each 1 ≤ κ ≤ n we construct a 2n − κ-dimensional linear space H(n, κ) of n × n Hankel matrices over F such that rank A ≥ κ for all 0 ≠ A ε H(n, κ). It follows that if W is a linear space of Hankel matrices over F such that rank A ≤ κ for all A ε W, then dim W ≤ κ.