Construction of quantum codes from (, ) -cyclic codes

Let Fq be the finite field of q=pᵐ elements where p is a prime and m is a positive integer. This paper considers (, ) -cyclic codes over a class of finite commutative non-chain rings Rₐ, ₒ=Fqv₁, v₂, , vₛ/ vᵢ-vᵢ², vᵢvⱼ=vⱼvᵢ=0 where is an automorphism of Rₐ, ₒ, is a -derivation of Rₐ, ₒ and 1 i j s for a positive integer s. Here, we show that a (, ) -cyclic code of length n over Rₐ, ₒ is the direct sum of (, ) -cyclic codes of length n over Fq, where is an automorphism of Fq and is a -derivation of Fq. Further, necessary and sufficient conditions for both (, ) -cyclic and (, ) -cyclic codes to contain their Euclidean duals are established. Finally, we obtain many quantum codes by applying the dual containing criterion on the Gray images of these codes. The obtained codes have better parameters than those available in the literature.