Related papers: Asymmetric and Symmetric Subsystem BCH Codes and B…
Quantum error correction was invented to allow for fault-tolerant quantum computation. Systems with topological order turned out to give a natural physical realization of quantum error correcting codes (QECC) in their groundspaces. More…
In this paper, we present two new ways of quantum synchronization coding based on the $(\bm{u}+\bm{v}|\bm{u}-\bm{v})$ construction and the product construction respectively, and greatly enrich the varieties of available quantum…
A general framework describing the statistical discrimination of an ensemble of quantum channels is given by the name of quantum reading. Several tools can be applied in quantum reading to reduce the error probability in distinguishing the…
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…
In this paper we extend to asymmetric quantum error-correcting codes (AQECC) the construction methods, namely: puncturing, extending, expanding, direct sum and the (u|u + v) construction. By applying these methods, several families of…
Subsystem codes are the most versatile class of quantum error-correcting codes known to date that combine the best features of all known passive and active error-control schemes. The subsystem code is a subspace of the quantum state space…
One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. In this paper, we first present a construction of classical codes based on certain class of polynomials. Through these classical…
The Bose-Chaudhuri-Hocquenghem (BCH) codes are a well-studied subclass of cyclic codes that have found numerous applications in error correction and notably in quantum information processing. A subclass of attractive BCH codes is the…
BCH codes are an important class of cyclic codes which have applications in satellite communications, DVDs, disk drives, and two-dimensional bar codes. Although BCH codes have been widely studied, their parameters are known for only a few…
Quantum synchronizable codes are quantum error-correcting codes designed to correct the effects of both quantum noise and block synchronization errors. While it is known that quantum synchronizable codes can be constructed from cyclic codes…
Cyclic codes are an interesting class of linear codes due to their efficient encoding and decoding algorithms as well as their theoretical importance. BCH codes form a subclass of cyclic codes and are very important in both theory and…
Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of error information--error syndromes. To obtain reliable error syndromes using imperfect physical circuits, we propose the idea…
Subsystem codes protect quantum information by encoding it in a tensor factor of a subspace of the physical state space. Subsystem codes generalize all major quantum error protection schemes, and therefore are especially versatile. This…
Four quantum code constructions generating several new families of good nonbinary quantum nonprimitive non-narrow-sense Bose-Chaudhuri-Hocquenghem (BCH) codes are presented in this paper. The first two ones are based on…
We investigate CSS and CSS-T quantum error-correcting codes from the point of view of their existence, rarity, and performance. We give a lower bound on the number of pairs of linear codes that give rise to a CSS code with good correction…
We define a new family of codes for symmetric classical-quantum channels and establish their optimality. To this end, we extend the classical notion of generalized perfect and quasi-perfect codes to channels defined over some finite…
This paper introduces a construction of quantum CSS codes from a tuple of component CSS codes and two collections of subsets. The resulting codes have parallelizable encoding and syndrome measurement circuits and built-in redundancy in the…
We prove several theorems characterizing the existence of homological error correction codes both classically and quantumly. Not every classical code is homological, but we find a family of classical homological codes saturating the Hamming…
Constacyclic codes are important classes of linear codes that have been applied to the construction of quantum codes. Six new families of asymmetric quantum codes derived from constacyclic codes are constructed in this paper. Moreover, the…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…