Non-binary quantum codes from constacyclic codes over 𝔽q[u1, u2,…,uk]/⟨ui3 = ui, uiuj = ujui⟩

Abstract

Let q=pmq={p}^{m}, pp be an odd prime, and Rk=Fq[u1,u2,…,uk]/⟨ui3=ui,uiuj=ujui⟩{R}_{k}={{\mathbb{F}}}_{q}\left[{u}_{1},{u}_{2},\ldots ,{u}_{k}]\hspace{-0.08em}\text{/}\hspace{-0.08em}\langle {u}_{i}^{3}={u}_{i},{u}_{i}{u}_{j}={u}_{j}{u}_{i}\rangle , where k≥1k\ge 1 and 1≤i,j≤k1\le i,j\le k. In this article, we define a Gray map from Rkn{R}_{k}^{n} to Fq3kn{{\mathbb{F}}}_{q}^{{3}^{k}n}. We study constacyclic codes over Rk{R}_{k} and construct non-binary quantum codes over Fq{{\mathbb{F}}}_{q}.

Keywords

• constacyclic codes
• quantum codes
• gray map
• dual-containing codes
• 94b05
• 94b15