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arxiv: 1711.03307 · v1 · pith:2MTB4GSJnew · submitted 2017-11-09 · 💻 cs.IT · math.IT

Self-Dual Cyclic and Quantum Codes Over Z2^(α) x (Z2 + uZ2)^(β)

classification 💻 cs.IT math.IT
keywords codescyclicquantumself-dualalphabetacodebinary
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In this paper we introduce self-dual cyclic and quantum codes over Z2^{\alpha} x (Z2 + uZ2)^{\beta}. We determine the conditions for any Z2Z2[u]-cyclic code to be self-dual, that is, C = C^{\perp}. Since the binary image of a self-orthogonal Z2Z2[u]-linear code is also a self-orthogonal binary linear code, we introduce quantum codes over Z2^{\alpha} x (Z2 + uZ2)^{\beta}. Finally, we present some examples of self-dual cyclic and quantum codes that have good parameters.

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