Spread Codes from Abelian non-cyclic groups

TL;DR

This paper introduces a novel method for constructing spreads in finite vector spaces using Abelian non-cyclic groups, resulting in orbit codes with maximum distance and complete spreads with orbital structure.

Contribution

It presents a new approach to constructing spreads via Abelian non-cyclic groups, including maximum distance orbit codes and complete spreads with orbital structure.

Findings

Constructed a family of maximum distance orbit codes.

Achieved complete spreads with orbital structure.

Provided a new algebraic framework for spreads in finite fields.

Abstract

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.