In this paper, we investigate the method of constructing quantum codes from cyclic codes over the ring
R=Fq+uFq+vFq (u2=u, v2=v, uv=vu=0). By means of the generator polynomials and some decomposition of cyclic codes and their dual over R, we give a necessary and sufficient condition of the cyclic codes over R to be construct the quantum codes. Also as an application, we obtain new non binary quantum codes from those classes of cyclic codes.
The purpose of this paper is to identify the structural characteristics and construction of quantum codes over
Fp using $\alpha_1+\alpha_2 {\mu}+\alpha_3 {\nu}+\alpha_4 {\varpi}+\alpha_5 {\mu}{\nu}+\alpha_6 {\nu}{\varpi}+\alpha_7 {\mu}{\varpi}+\alpha_8 {\mu}{\nu}{\varpi}- $constacyclic codes over ring
R = Fp[μ,ν,ϖ]/<μ2−μ,ν2−ν,ϖ2−ϖ ,μν−νμ,νϖ−ϖν,μϖ−ϖμ>, here
Fp is a finite field with p elements. We define a Gray map from
R to
Fp8, a distance-preserving map. Breaking down constacyclic codes into cyclic and negacyclic codes results in the creation of quantum codes over the finite field
Fp. As an application, some examples are illustrated to obtain the quantum codes of different parameters.
In this article, for a finite field
Fq and a natural number
l, let
R denote the product ring
Fql. Firstly, for an automorphism
Θ of
R, a
Θ-derivation
ΔΘ of
R and for a unit
a in
R, we study
(Θ,ΔΘ,a)-cyclic codes over
R. In this direction, we give an algebraic characterization of a
(Θ,ΔΘ,a)-cyclic code over
R, determine its generator polynomial, and find its decomposition over
Fq. Secondly, we give a necessary and sufficient condition for a
(Θ,0,a)-cyclic code to be Euclidean dual-containing code over
R. Thirdly, we study Gray maps and obtain several MDS and optimal linear codes over
Fq as Gray images of
(Θ,ΔΘ,a)-cyclic codes over
R. Moreover, we determine orthogonality preserving Gray maps and construct Euclidean dual-containing codes with good parameters. Lastly, as an application, we construct MDS and almost MDS quantum codes by employing the Euclidean dual-containing and annihilator dual-containing CSS constructions.