Multilevel Quantum Error Correction Codes in Transform Domain

Quantum error correction codes (QECC) have become cornerstone of quantum information and computation. In this correspondence, we investigate a class of QECC in transform domain. To design the QECC denoted by [[N, k, d]] with larger N, generators of stabilizer of the constructed codes are composed via selecting randomly N - k rows from an yielded matrices with recursive relations of matrices transform. Subsequently, a new kind of stabilizer quantum codes may be generated expediently. In the proposed approach, the parameter N may be arbitrary larger, and the QECC with larger N may be easily constructed due to the employment of the recursive relations of matrices transform. Especially, some new codes, which are impossible to be obtained via the previous approaches, are constructed. The resulting codes are more efficient with better perimeters than the previous quantum codes.