Quantum Synchronizable Codes From Augmentation of Cyclic Codes

We propose a new method to construct quantum synchronizable codes from classical cyclic codes using the idea of augmented cyclic codes. The method augments a dual-containing cyclic code C2 to obtain another cyclic codes C1 of higher dimension. The resulting two cyclic codes and the dual code C⊥ 2 satisfy the containing property C⊥ 2 ⊂ C2 ⊂ C1. The proposed construction method based on general quadratic residue sets of size p = 2 − 1, such that the constructed quantum synchronizable codes are Calderbank-Shor-Steane (CSS) quantum error correcting codes. We show that the proposed construction method yield (cl, cr)− [[p+cl+cr, 1]] quantum synchronizable codes that can tolerate maximum number of misalignment errors.