Related papers: The Subfield Metric and its Application to Quantum…
This paper computationally obtains optimal bounded-weight, binary, error-correcting codes for a variety of distance bounds and dimensions. We compare the sizes of our codes to the sizes of optimal constant-weight, binary, error-correcting…
The problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model. For coherent network coding, where knowledge of the network topology and network code is assumed at the source and…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
Quantum error correction of a surface code or repetition code requires the pairwise matching of error events in a space-time graph of qubit measurements, such that the total weight of the matching is minimized. The input weights follow from…
Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels.…
We present a construction scheme for quantum error correcting codes. The basic ingredients are a graph and a finite abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph…
A lower bound on the number of uncorrectable errors of weight half the minimum distance is derived for binary linear codes satisfying some condition. The condition is satisfied by some primitive BCH codes, extended primitive BCH codes,…
This work develops a geometric framework for constructing quantum error-correcting codes from weighted projective and orbifold structures, integrating algebraic geometry, divisor theory, and the CSS stabilizer formalism. Beginning with…
In many physical systems it is expected that environmental decoherence will exhibit an asymmetry between dephasing and relaxation that may result in qubits experiencing discrete phase errors more frequently than discrete bit errors. In the…
We present a universal framework for quantum error-correcting codes, i.e., the one that applies for the most general quantum error-correcting codes. This framework is established on the group algebra, an algebraic notation for the nice…
Bounds on linear codes play a central role in coding theory, as they capture the fundamental trade-off between error-correction capability (minimum distance) and information rate (dimension relative to length). Classical results…
The problem of finding quantum error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are…
Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an…
Given that approximate quantum error-correcting (AQEC) codes have a potentially better performance than perfect quantum error correction codes, it is pertinent to quantify their performance. While quantum weight enumerators establish some…
While quantum weight enumerators establish some of the best upper bounds on the minimum distance of quantum error-correcting codes, these bounds are not optimized to quantify the performance of quantum codes under the effect of arbitrary…
Quantum weight reduction is the task of transforming a quantum code with large check weight into one with small check weight. Low-weight codes are essential for implementing quantum error correction on physical hardware, since high-weight…
A quantum code is a subspace of a Hilbert space of a physical system chosen to be correctable against a given class of errors, where information can be encoded. Ideally, the quantum code lies within the ground space of the physical system.…
The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous…
We point out a general framework that encompasses most cases in which quantum effects enable an increase in precision when estimating a parameter (quantum metrology). The typical quantum precision-enhancement is of the order of the square…
This work introduces a symplectic framework for quantum error correcting codes in which local structure is analyzed through an anticode perspective. In this setting, a code is treated as a symplectic space, and anticodes arise as maximal…