T-Direct codes: an application to T-user BAC

A T-Direct code is defined as the set of T F-ary linear codes Γ₁, Γ₂, ..., Γ_T such that Γ_i ∩ Γ_i^⊥={0} for each i, where Γ_i^⊥= Γ₁ ⊕ Γ₂ ⊕···⊕ Γ_i-1 ⊕ Γ_i+1 ⊕···⊕ Γ_T is the dual of Γ_i with respect to the direct sum Λ= Γ₁ ⊕ Γ₂ ⊕···⊕ Γ_T. An algebraic characterization to this class of codes is given. An application of T-Direct codes to the noiseless T-user binary adder channel is also presented.