Index
A
Adele, 54
Adjoint of a matrix, 9
Affine-invariant code, 159
Algebraic function field, 53
Algebraic geometry code, 55
Anti-commutator, 14, 15
Asymmetric quantum codes, 128
Asymptotically good codes, 113
B
Basic generator matrix, 164
Basis, 3
BCH bound Theorem, 51
BCH code, 52
Bilinear function, 6
Binary Hamming code, 44
Block codes, 43
C
Canonical divisor, 55
Catastrophic matrix, 164
Cauchy sequence, 9
Center of a group, 37
Centralizer of a subgroup, 37
Character code, 155
Characteristic polynomial, 5
CNOT gate, 22
Code expansion, 48
Commutator, 14, 15
Completeness equation, 17
Complex conjugate, 9
Complex vector space, 9
Convergence of sequences, 9
Convolutional code, 164
CSS construction, 38
CSS-like construction, 167
Cyclic code, 51
Cyclotomic coset, 52
D
Defining set, 52
Defining set of a cyclic code, 58
Defining set of a negacyclic code, 186
Degree of a convolutional code, 164
Degree of a divisor, 54
Degree of a quantum convolutional code,
166
Density operator, 18
Depolarizing channel, 23
Diagonalizable operator, 5
Dimension, 3
Dirac notation, 9
Direct product code, 49
Direct sum code, 49
Discrete valuation, 53
Distance function, 8
Divisor, 53, 54
Dual basis of F q m over F q , 48
E
Eigenspace, 4
Eigenvalue, 4, 5
Eigenvector, 4
Ensemble of quantum states, 18
Equivalence of codes, 51
Euclidean dual code, 46
Euclidean dual of an AG code, 56
Euclidean inner product, 46
Euclidean space, 8
© Springer Nature Switzerland AG 2020
G. G. La Guardia, Quantum Error Correction, Quantum Science and Technology,
https://doi.org/10.1007/978-3-030-48551-1
225