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A construction of quantum LDPC codes from Cayley graphs

Abstract : We study a construction of Quantum LDPC codes proposed by MacKay, Mitchison and Shokrollahi in the draft [6]. It is based on the Cayley graph of F_2^n 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 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-1}, 2^{n/2}, 2^{n/2-1}]].
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Submitted on : Friday, December 13, 2013 - 8:07:08 AM
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Alain Couvreur, Nicolas Delfosse, Gilles Zemor. A construction of quantum LDPC codes from Cayley graphs. IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2013, 59 (9), pp.6087-6098. ⟨10.1109/TIT.2013.2261116⟩. ⟨hal-00632257v4⟩



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