Erratum to: "Fast quantum codes based on Pauli block Jacket matrices"

Fast circulant block Jacket transform based on the Pauli matrices

Owing to its orthogonality, simplicity of the inversion and fast algorithms, Jacket transform generalising from the Hadamard transform has played important roles in signal and image processing, mobile communication for coding design, cryptography, etc. In this paper, inspired by the emerging block Jacket transform, a new class of circulant block Jacket matrices (CBJMs) are mathematically define...

Fast Constructions of Quantum Codes Based on Residues Pauli Block Matrices

Arikan and Alamouti matrices based on fast block-wise inverse jacket transform

Recently, Lee and Hou (IEEE Signal Process Lett 13: 461-464, 2006) proposed one-dimensional and two-dimensional fast algorithms for block-wise inverse Jacket transforms (BIJTs). Their BIJTs are not real inverse Jacket transforms from mathematical point of view because their inverses do not satisfy the usual condition, i.e., the multiplication of a matrix with its inverse matrix is not equal to ...

Is A Quantum Stabilizer Code Degenerate or Nondegenerate for Pauli Channel?

core of quantum decoding network and is also the key step of recovery. The definitions of the bit-flip error syndrome matrix and the phase-flip error syndrome matrix were presented, and then the error syndromes of quantum errors were expressed in terms of the columns of the bit-flip error syndrome matrix and the phase-flip error syndrome matrix. It also showed that the error syndrome matrices o...

An explicit construction of fast cocyclic jacket transform on the finite field with any size

An orthogonal cocyclic framework of the block-wise inverse Jacket transform (BIJT) is proposed over the finite field. Instead of the conventional block-wise inverse Jacket matrix (BIJM), we investigate the cocyclic block-wise inverse Jacket matrix (CBIJM), where the high-order CBIJM can be factorized into the low-order sparse CBIJMs with a successive block architecture. It has a recursive fashi...