Related papers: Quantum Cyclic Code
In this article, we investigate properties of cyclic codes over a finite non-chain ring $\mathbb{F}_q+v\mathbb{F}_q+v^2\mathbb{F}_q+v^3\mathbb{F}_q+v^4\mathbb{F}_q,$ where $q=p^r,$ $r$ is a positive integer, $p$ is an odd prime, $4 \mid…
For a number of quantum channels of interest, phase-flip errors occur far more frequently than bit-flip errors. When transmitting across these asymmetric channels, the decoding error rate can be reduced by tailoring the code used to the…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
Cyclicity of a convolutional code (CC) is relying on a nontrivial automorphism of the algebra F[x]/(x^n-1), where F is a finite field. If this automorphism itself has certain specific cyclicity properties one is lead to the class of…
Quantum synchronizable error-correcting codes are special quantum error-correcting codes that are designed to correct both the effect of quantum noise on qubits and misalignment in block synchronization. It is known that in principle such a…
Classical BCH codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes; this correspondence studies the properties of such codes. It is shown that a BCH code of length n can contain its…
We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes. Using this result --…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Let $m=2\ell+1$ for an integer $\ell\geq 1$…
The concept of generalized concatenated quantum codes (GCQC) provides a systematic way for constructing good quantum codes from short component codes. We introduce a stabilizer formalism for GCQCs, which is achieved by defining quantum…
We describe a class of "neighboring-blocks" stabilizer quantum error correction codes and demonstrate that such class of codes can be implemented in a resource-efficient manner using a single ancilla and circular near-neighbor qubit…
Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems and communication systems as they have efficient encoding and decoding algorithms. In this paper, we settle an open problem…
The realization of quantum error correction protocols whose logical error rates are suppressed far below physical error rates relies on an intricate combination: the error-correcting code's efficiency, the syndrome extraction circuit's…
We characterize the affine-invariant maximal extended cyclic codes. Then by the CSS construction, we derive from these codes a family of pure quantum codes. Also for ordnq even, a new family of degenerate quantum stabilizer codes is derived…
Subspace codes and particularly constant dimension codes have attracted much attention in recent years due to their applications in random network coding. As a particular subclass of subspace codes, cyclic subspace codes have additional…
Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible. Quantum LDPC codes range from…
Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored…
We use affine variety codes and their subfield-subcodes for obtaining quantum stabilizer codes via the CSS code construction. With this procedure, we get codes with good parameters and a code whose parameters exceed the CSS quantum…
We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…
Implementing robust quantum error correction (QEC) is imperative for harnessing the promise of quantum technologies. We introduce a framework that takes {\it any} classical code and explicitly constructs the corresponding QEC code. Our…