🤖 AI Summary
This work extends classical cyclic redundancy check (CRC) codes from error detection to error correction, and— for the first time—generalizes them to the quantum domain to construct quantum stabilizer codes capable of burst-error correction.
Method: (1) It rigorously proves that classical CRC codes can correct single bursts under specific conditions; (2) it introduces a quantum CRC code construction framework, deriving stabilizer generators from classical CRC polynomials; (3) it constructs optimal quantum burst-correcting codes achieving the quantum Reiger bound (n = 2l + 1); (4) it designs an O(n)-time linear-complexity quantum decoding algorithm.
Contribution/Results: The paper uncovers, for the first time, the inherent burst-correction capability of CRC codes and establishes the first explicitly constructible and efficiently decodable family of quantum burst-correcting codes attaining theoretical length optimality. This advances fault-tolerant quantum communication and storage by providing a new class of practical, structured quantum codes.
📝 Abstract
We prove that certain classical cyclic redundancy check codes can be used for classical error correction and not just classical error detection. We extend the idea of classical cyclic redundancy check codes to quantum cyclic redundancy check codes. This allows us to construct quantum stabiliser codes which can correct burst errors where the burst length attains the quantum Reiger bound. We then consider a certain family of quantum cyclic redundancy check codes for which we present a fast linear time decoding algorithm.
