相关论文: Narain CFTs and error-correcting codes on finite f…

We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ with symmetric generator matrices from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$. Using this method, we improve the…

When data is stored, compressed, or communicated through a media such as cable or air, sources of noise and other parameters such as EMI, crosstalk, and distance can considerably affect the reliability of these data. Error detection and…

Quantum computing based on Neutral Atoms (NAs) provides a wide range of computational capabilities, encompassing high-fidelity long-range interactions with native multi-qubit gates, and the ability to shuttle arrays of qubits. While…

We propose a prescription for describing correlation functions in higher-dimensional defect conformal field theories (DCFTs) by those in ancillary conformal field theories (CFTs) without defects, which is a vast generalization of the image…

In this paper, we construct self-dual codes from a construction that involves 2x2 block circulant matrices, group rings and a reverse circulant matrix. We provide conditions whereby this construction can yield self-dual codes. We construct…

Spatially-coupled (SC) codes are a family of graph-based codes that have attracted significant attention thanks to their capacity approaching performance and low decoding latency. An SC code is constructed by partitioning an underlying…

Recently, two-dimensional (2D) array codes have been found to have applications in wireless communication.In this paper, we propose direct construction of 2D complete complementary codes (2D-CCCs) with arbitrary array size and flexible set…

We show how to construct unramified qoaternion extensions of quadratic number fields.

Researchers from a broad spectrum of scientific and engineering disciplines are increasingly using near-field infrared spectroscopic techniques to characterize materials nondestructively and with nanoscale spatial resolution. However,…

This paper introduces techniques to construct binary polar source/channel codes based on the bit error probability of successive-cancellation decoding. The polarization lemma is reconstructed based on the bit error probability and then…

We investigate weakly constrained codes, in which specific patterns occur with prescribed frequencies rather than being strictly forbidden as in conventional constrained coding. We propose a capacity-achieving construction of a weakly…

Erasure codes have emerged as an efficient technology for providing data redundancy in distributed storage systems. However, it is a challenging task to repair the failed storage nodes in erasure-coded storage systems, which requires large…

Existing construction algorithms of block network-error correcting codes require a rather large field size, which grows with the size of the network and the number of sinks, and thereby can be prohibitive in large networks. In this work, we…

We investigate the conformal algebra on the fuzzy sphere, and in particular the generators of translations and special conformal transformations which are emergent symmetries in the infinite IR but are broken along the RG flow. We show how…

This paper gives new methods of constructing {\it symmetric self-dual codes} over a finite field $GF(q)$ where $q$ is a power of an odd prime. These methods are motivated by the well-known Pless symmetry codes and quadratic double circulant…

We consider linear codes over a field in which the error values are restricted to a subgroup of its unit group. This scenario captures Lee distance codes as well as codes over the Gaussian or Eisenstein integers. Codes correcting restricted…

Quantum Fourier Transform (QFT) plays a principal role in the development of efficient quantum algorithms. Since the number of quantum bits that can currently built is limited, while many quantum technologies are inherently three- (or more)…

In the current paper we provide a proof of NP-completeness for the CFP problem with the fractional grouping efficacy objective. For this purpose we first consider the CFP with the linear objective minimizing the total number of exceptions…

This work shows several direct and recursive constructions of ordered covering arrays using projection, fusion, column augmentation, derivation, concatenation and cartesian product. Upper bounds on covering codes in NRT spaces are also…

Neural Network Field Theories (NN-FTs) represent a novel construction of arbitrary field theories, including those of conformal fields, through the specification of the network architecture and prior distribution for the network parameters.…