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New quantum codes from dual-containing cyclic codes over finite rings.
- Source :
-
Quantum Information Processing . Nov2016, Vol. 15 Issue 11, p4489-4500. 12p. - Publication Year :
- 2016
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CYCLIC codes
*FINITE rings
*BINARY codes
*QUANTUM states
*FINITE fields
Subjects
Details
- Language :
- English
- ISSN :
- 15700755
- Volume :
- 15
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Quantum Information Processing
- Publication Type :
- Academic Journal
- Accession number :
- 118988965
- Full Text :
- https://doi.org/10.1007/s11128-016-1426-5