Quantum Block and Convolutional Codes from Self-orthogonal Product Codes
arXiv:quant-ph/0703181 · doi:10.1109/ISIT.2005.1523493
Abstract
We present a construction of self-orthogonal codes using product codes. From the resulting codes, one can construct both block quantum error-correcting codes and quantum convolutional codes. We show that from the examples of convolutional codes found, we can derive ordinary quantum error-correcting codes using tail-biting with parameters [[42N,24N,3]]_2. While it is known that the product construction cannot improve the rate in the classical case, we show that this can happen for quantum codes: we show that a code [[15,7,3]]_2 is obtained by the product of a code [[5,1,3]]_2 with a suitable code.
5 pages, paper presented at the 2005 IEEE International Symposium on Information Theory
References in corpus (6)
Cited by in corpus (15)
- Non-catastrophic Encoders and Encoder Inverses for Quantum Convolutional Codes
- Improved quantum hypergraph-product LDPC codes
- The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
- Quantum Convolutional BCH Codes
- Constructions of Quantum Convolutional Codes
- On Classical and Quantum MDS-Convolutional BCH Codes
- Quantum Convolutional Codes Derived From Reed-Solomon and Reed-Muller Codes
- A Construction of MDS Quantum Convolutional Codes
- Asymmetric Quantum Concatenated and Tensor Product Codes with Large Z-Distances
- On Quantum and Classical Error Control Codes: Constructions and Applications
- Convolutional codes from unit schemes
- Linear block and convolutional MDS codes to required rate, distance and type
- On Quantum Tensor Product Codes
- New constructions of quantum MDS convolutional codes derived from generalized Reed-Solomon codes
- Quantum Error Source and Channel Coding