Construction of Singer subgroup orbit codes based on cyclic difference sets

A construction of Abelian non-cyclic orbit codes

“…Assume that q = p r is a prime power and let k and n be nonnegative integers satisfying inequalities of expression (8). Assume also that λ ∈ F q is a primitive element.…”

“…Assume that q = p r is a prime power and let k and n be nonnegative integers satisfying the inequalities in expression (8). Then, p r−1 + 1 ≤ k ≤ p r−1 (p − 1) and p r−1 + 2k ≤ n ≤ p r + k.…”

“…The paper at hand is most closely related to references [2,8,9,19,20,24,25,26]. All these papers deal with orbit codes, which are constant dimension codes that arise as an orbit of a subspace in F n q under the action of a subgroup of the general linear group.…”