On Quantum Codes Obtained from Cyclic Codes over A2

Abstract

In this paper, quantum codes from cyclic codes over A<inf>2</inf> = F<inf>2</inf> + uF<inf>2</inf> + vF<inf>2</inf> + uvF<inf>2</inf>, u2 = u, v2 = v, uv = vu, for arbitrary length n have been constructed. It is shown that if C is self orthogonal over A<inf>2</inf>, then so is ψ(C), where ψ is a Gray map. A necessary and sufficient condition for cyclic codes over A<inf>2</inf> that contains its dual has also been given. Finally, the parameters of quantum error correcting codes are obtained from cyclic codes over A<inf>2</inf>. © 2015 World Scientific Publishing Company.