7 papers · 1 filter
Dualities of dihedral and generalised quaternion codes and applications to quantum codes
Miguel Sales-Cabrera, Xaro Soler-Escrivà, Víctor Sotomayor
Let be a finite field of elements, for some prime power , and let be a finite group. A (left) group code, or simply a -code, is a (left) ideal of the g…
Spread Codes from Abelian non-cyclic groups
Joan-Josep Climent, Veronica Requena, Xaro Soler-Escrivà
Given the finite field , for a prime power , in this paper we present a way of constructing spreads of . They will arise as orbits under the…
Codes in algebras of direct products of groups
Miguel Sales-Cabrera, Xaro Soler-Escrivà, Víctor Sotomayor
In this paper we obtain the Wedderburn-Artin decomposition of a semisimple group algebra associated to a direct product of finite groups. We also provide formulae for the number of…
Equivalence for flag codes
Miguel Ángel Navarro-Pérez, Xaro Soler-Escrivà
Given a finite field F_q and a positive integer n, a flag is a sequence of nested F_q-subspaces of a vector space F_q^n and a flag code is a nonempty collection of flags. The proje…
An Orbital Construction of Optimum Distance Flag Codes
Clementa Alonso-González, Miguel Ángel Navarro-Pérez, Xaro Soler-Escrivà
Flag codes are multishot network codes consisting of sequences of nested subspaces (flags) of a vector space , where is a prime power and , the fi…
Optimum Distance Flag Codes from Spreads via Perfect Matchings in Graphs
Clementa Alonso-González, Miguel Ángel Navarro-Pérez, Xaro Soler-Escrivà
In this paper, we study flag codes on the vector space , being a prime power and the finite field of elements. More precisely, we focus on fl…