相关论文: Decoding method for generalized algebraic geometry…
We provide a theoretical study of Algebraic Geometry codes constructed from abelian surfaces defined over finite fields. We give a general bound on their minimum distance and we investigate how this estimation can be sharpened under the…
We compare the performance of short-length linear binary codes on the binary erasure channel and the binary-input Gaussian channel. We use a universal decoder that can decode any linear binary block code: Gaussian-elimination based…
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…
In this paper, we first propose a general interpolation algorithm in a free module of a linearized polynomial ring, and then apply this algorithm to decode several important families of codes, Gabidulin codes, KK codes and MV codes. Our…
For an integer $s\ge 1$, let $\mathcal{C}_s(q_0)$ be the generalized Zetterberg code of length $q_0^s+1$ over the finite field $\F_{q_0}$ of odd characteristic. Recently, Shi, Helleseth, and \"{O}zbudak (IEEE Trans. Inf. Theory 69(11):…
Fracton topological phases have a large number of materialized symmetries that enforce a rigid structure on their excitations. Remarkably, we find that the symmetries of a quantum error-correcting code based on a fracton phase enable us to…
This paper presents a polarization-driven (PD) shortening technique for the design of rate-compatible polar codes. The proposed shortening strategy consists of reducing the generator matrix by relating its row index with the channel…
Foliated quantum codes are a resource for fault-tolerant measurement-based quantum error correction for quantum repeaters and for quantum computation. They represent a general approach to integrating a range of possible quantum error…
The surface code is one of the most promising candidates for combating errors in large scale fault-tolerant quantum computation. A fault-tolerant decoder is a vital part of the error correction process---it is the algorithm which computes…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
Generalized quasi-cyclic (GQC) codes form a natural generalization of quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a family of ring alphabets. Decomposing these rings into local rings by the Chinese Remainder…
The constituent parts of a quantum computer are inherently vulnerable to errors. To this end we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a…
We demonstrate a construction of error-correcting codes from graphs by means of $k$-resolving sets, and present a decoding algorithm which makes use of covering designs. Along the way, we determine the $k$-metric dimension of grid graphs…
Permutation codes have recently garnered substantial research interest due to their potential in various applications including cloud storage systems, genome resequencing and flash memories. In this paper, we study the theoretical bounds…
This work introduces a decoding strategy for binary self-dual codes possessing an automorphism of a specific type. The proposed algorithm is a hard decision iterative decoding scheme. The enclosed experiments show that the new decoding…
We study a generalization of deduplication, which enables lossless deduplication of highly similar data and show that standard deduplication with fixed chunk length is a special case. We provide bounds on the expected length of coded…
Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, have a special place in algebraic coding theory. Among other things, many of the best-known or optimal codes have been obtained from these classes. In this…
Polarization-adjusted convolutional (PAC) codes were recently proposed and arouse the interest of the channel coding community because they were shown to approach theoretical bounds for the (128,64) code size. In this letter, we propose…
In this paper we introduce a new right preprocessing method for the decoding of 2x2 algebraic STBCs, called algebraic reduction, which exploits the multiplicative structure of the code. The principle of the new reduction is to absorb part…
Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters. In this paper, for…