Open Mathematics (Sep 2022)
Non-binary quantum codes from constacyclic codes over š½q[u1, u2,ā¦,uk]/āØui3 = ui, uiuj = ujuiā©
Abstract
Let q=pmq={p}^{m}, pp be an odd prime, and Rk=Fq[u1,u2,ā¦,uk]/āØui3=ui,uiuj=ujuiā©{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 kā„1k\ge 1 and 1ā¤i,jā¤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}.
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