Spread Codes from Abelian non-cyclic groups

Given the finite field $\mathbb{F}_{q}$, for a prime power $q$, in this paper we present a way of constructing spreads of $\mathbb{F}_{q}^{n}$. They will arise as orbits under the action of an Abelian non-cyclic group. First, we construct a family of orbit codes of maximum distance using this group, and then we complete each of these codes to achieve a spread of the whole space having an orbital structure.