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- Title
New quantum codes from dual-containing cyclic codes over finite rings.
- Authors
Tang, Yongsheng; Zhu, Shixin; Kai, Xiaoshan; Ding, Jian
- Abstract
Let $$R=\mathbb {F}_{2^{m}}+u\mathbb {F}_{2^{m}}+\cdots +u^{k}\mathbb {F}_{2^{m}}$$ , where $$\mathbb {F}_{2^{m}}$$ is the finite field with $$2^{m}$$ elements, m is a positive integer, and 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. In particular, 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.
- Subjects
CYCLIC codes; FINITE rings; BINARY codes; QUANTUM states; FINITE fields
- Publication
Quantum Information Processing, 2016, Vol 15, Issue 11, p4489
- ISSN
1570-0755
- Publication type
Article
- DOI
10.1007/s11128-016-1426-5