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arXiv · 1206.2656

A Construction of Quantum LDPC Codes from Cayley Graphs

Alain Couvreur·Nicolas Delfosse·Gilles Zémor
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Abstract

We study a construction of Quantum LDPC codes proposed by MacKay, Mitchison and Shokrollahi. It is based on the Cayley graph of Fn together with a set of generators regarded as the columns of the parity-check matrix of a classical code. We give a general lower bound on the minimum distance of the Quantum code in $\mathcal{O}(dn^2)$ where d is the minimum distance of the classical code. When the classical code is the $[n, 1, n]$ repetition code, we are able to compute the exact parameters of the associated Quantum code which are $[[2^n, 2^{\frac{n+1}{2}}, 2^{\frac{n-1}{2}}]]$.

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Alain Couvreur, Nicolas Delfosse, Gilles Zémor. 2013-12-17. A Construction of Quantum LDPC Codes from Cayley Graphs. https://arxiv.org/abs/1206.2656

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