Quantum Convolutional BCH Codes
arXiv:quant-ph/0703113 · doi:10.1109/CWIT.2007.375730
Abstract
Quantum convolutional codes can be used to protect a sequence of qubits of arbitrary length against decoherence. We introduce two new families of quantum convolutional codes. Our construction is based on an algebraic method which allows to construct classical convolutional codes from block codes, in particular BCH codes. These codes have the property that they contain their Euclidean, respectively Hermitian, dual codes. Hence, they can be used to define quantum convolutional codes by the stabilizer code construction. We compute BCH-like bounds on the free distances which can be controlled as in the case of block codes, and establish that the codes have non-catastrophic encoders.
4 pages, minor changes, accepted for publication at the 10th Canadian Workshop on Information Theory (CWIT'07)
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- Quantum Convolutional Coding with Shared Entanglement: General Structure
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- Asymmetric and Symmetric Subsystem BCH Codes and Beyond
- New Convolutional Codes Derived from Algebraic Geometry Codes
- Minimal-memory realization of pearl-necklace encoders of general quantum convolutional codes
- On Quantum and Classical Error Control Codes: Constructions and Applications
- Examples of minimal-memory, non-catastrophic quantum convolutional encoders
- Linear block and convolutional MDS codes to required rate, distance and type
- Convolutional Codes Derived From Group Character Codes
- Asymmetric quantum convolutional codes
- New constructions of quantum MDS convolutional codes derived from generalized Reed-Solomon codes