Quantum codes from constacyclic codes over S_{k}

Abstract

Let S_{k}={mathbb{F}}_{q}[u_{1},u_{2},ldots ,u_{k}]/langle u^{3}_{i}=u_{i},u_{i}u_{j}=u_{j}u_{i}=0 rangle , where 1leq i,jleq k, q=p^{m}, p is an odd prime. First, we define two new Gray maps phi _{k} and varphi _{k}, and study their Gray images. Further, we determine the structure of constacyclic codes and their dual codes, and give a necessary and sufficient conditions of constacyclic codes to contain their duals. Finally, we obtain some new quantum codes over mathbb{F}_{q} by using CSS construction, and compare the constructed codes better than the existing literature.