A construction of quantum LDPC codes from Cayley graphs
COUVREUR, Alain
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
Geometry, arithmetic, algorithms, codes and encryption [GRACE]
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
Geometry, arithmetic, algorithms, codes and encryption [GRACE]
COUVREUR, Alain
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
Geometry, arithmetic, algorithms, codes and encryption [GRACE]
< Reduce
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
Geometry, arithmetic, algorithms, codes and encryption [GRACE]
Language
en
Article de revue
This item was published in
IEEE Transactions on Information Theory. 2013-09, vol. 59, n° 9, p. 6087-6098
Institute of Electrical and Electronics Engineers
English 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 ...Read more >
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}]].Read less <
Origin
Hal imported