# Coding Theory

Linear Codes over Finite FieldsLinear code constructors, generator matrices and parameters.

[Linear Codes over Finite Fields](LinearCodes/index-linear-codes.md)Algebraic-Geometric CodesCodes constructed from algebraic curves, and their decoding.

[Algebraic-Geometric Codes](AlgebraicGeometricCodes/index-algebraic-geometric-codes.md)Low Density Parity Check CodesLDPC code construction and properties.

[Low Density Parity Check Codes](LowDensityParityCheckCodes/index-low-density-parity-check-codes.md)Linear Codes over Finite RingsLinear codes over finite rings: creation, subcodes and Boolean operations.

[Linear Codes over Finite Rings](LinearCodesOverFiniteRings/index-linear-codes-over-finite-rings.md)Linear Codes over the Integer Residue Ring Z4Linear codes over :math:`\mathbb{Z}_4`, invariants, weight enumerators and decoding.

[Linear Codes over the Integer Residue Ring {\mathbb{Z}}_4](LinearCodesOverZ4/index-linear-codes-over-z4.md)Additive CodesAdditive code constructors, subcodes and Boolean operations.

[Additive Codes](AdditiveCodes/index-additive-codes.md)Quantum CodesQuantum error-correcting codes, inner products and code combination.

[Quantum Codes](QuantumCodes/index-quantum-codes.md)