Quantum LDPC codes with positive rate and minimum distance proportional to $n^{1/2}$

Jean-Pierre Tillich (1) , Gilles Zémor (2)

1 SECRET - Security, Cryptology and Transmissions
2 IMB - Institut de Mathématiques de Bordeaux

The current best asymptotic lower bound on the minimum distance of quantum LDPC codes with fixed nonzero rate is logarithmic in the blocklength. We build quantum LDPC codes with fixed non-zero rate and prove that their minimum distance grows proportionally to the square root of the blocklength.

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Physique Quantique [quant-ph]

Jean-Pierre Tillich, Gilles Zémor. Quantum LDPC codes with positive rate and minimum distance proportional to $n^{1/2}$. IEEE Symposium on Information Theory, ISIT 2009, 2009, Seoul, South Korea. pp.799--804, ⟨10.1109/ISIT.2009.5205648⟩. ⟨hal-00776266⟩