On quantum codes obtained from cyclic codes over A(2)

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Dertli A., ÇENGELLENMİŞ Y., Eren Ş.

INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, vol.13, no.3, 2015 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 13 Issue: 3
• Publication Date: 2015
• Doi Number: 10.1142/s0219749915500318
• Journal Name: INTERNATIONAL JOURNAL OF QUANTUM INFORMATION
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Keywords: Quantum codes, cyclic codes, finite rings
• Ondokuz Mayıs University Affiliated: Yes

Abstract

In this paper, quantum codes from cyclic codes over A(2) = F-2 + uF(2) + vF(2) + uvF(2), u(2) = u, v(2) = v, uv = vu, for arbitrary length n have been constructed. It is shown that if C is self orthogonal over A(2), then so is Psi(C), where Psi is a Gray map. A necessary and sufficient condition for cyclic codes over A(2) that contains its dual has also been given. Finally, the parameters of quantum error correcting codes are obtained from cyclic codes over A(2).