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- W2949662218 abstract "Let $R=mathbb{F}_{2^{m}}+umathbb{F}_{2^{m}}+cdots+u^{k}mathbb{F}_{2^{m}}$ , where $mathbb{F}_{2^{m}}$ is a finite field with $2^{m}$ elements, $m$ is a positive integer, $u$ is an indeterminate with $u^{k+1}=0.$ In this paper, we propose the constructions of two new families of quantum codes obtained from dual-containing cyclic codes of odd length over $R$. A new Gray map over $R$ is defined and a sufficient and necessary condition for the existence of dual-containing cyclic codes over $R$ is given. A new family of $2^{m}$-ary quantum codes is obtained via the Gray map and the Calderbank-Shor-Steane construction from dual-containing cyclic codes over $R.$ Furthermore, a new family of binary quantum codes is obtained via the Gray map, the trace map and the Calderbank-Shor-Steane construction from dual-containing cyclic codes over $R.$" @default.
- W2949662218 created "2019-06-27" @default.
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- W2949662218 date "2016-08-23" @default.
- W2949662218 modified "2023-10-18" @default.
- W2949662218 title "New quantum codes from dual-containing cyclic codes over finite rings" @default.
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- W2949662218 doi "https://doi.org/10.48550/arxiv.1608.06674" @default.
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