Related papers: Decoding Algorithms for Two-dimensional Constacycl…
Topological codes have many desirable properties that allow fault-tolerant quantum computation with relatively low overhead. A core challenge for these codes, however, is to achieve a low-overhead universal gate set with limited…
This paper proposes Fulcrum network codes, a network coding framework that achieves three seemingly conflicting objectives: (i) to reduce the coding coefficient overhead to almost n bits per packet in a generation of n packets; (ii) to…
We analyze the performance of decoders for the 2D and 4D toric code which are local by construction. The 2D decoder is a cellular automaton decoder formulated by Harrington which explicitly has a finite speed of communication and…
We ask what is the general framework for a quantum error correcting code that is defined by a sequence of measurements. Recently, there has been much interest in Floquet codes and space-time codes. In this work, we define and study the…
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…
Attentional mechanisms are order-invariant. Positional encoding is a crucial component to allow attention-based deep model architectures such as Transformer to address sequences or images where the position of information matters. In this…
The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small…
We formulate mold filling in metal casting as a 2D neural operator learning problem that maps geometry and boundary data on an unstructured mesh to time resolved flow quantities, replacing expensive transient CFD. In the proposed method, a…
In this work we analyze the problem of phase retrieval from Fourier measurements with random diffraction patterns. To this end, we consider the recently introduced PhaseLift algorithm, which expresses the problem in the language of convex…
The graph fractional Fourier transform (GFRFT) applies a single global fractional order to all graph frequencies, which restricts its adaptability to diverse signal characteristics across the spectral domain. To address this limitation, in…
In this paper we study flag codes on $\mathbb{F}_q^n$, being $\mathbb{F}_q$ the finite field with $q$ elements. Special attention is given to the connection between the parameters and properties of a flag code and the ones of a family of…
Image subtraction is essential for transient detection in time-domain astronomy. The point spread function (PSF), photometric scaling, and sky background generally vary with time and across the field-of-view for imaging data taken with…
The Fast Fourier Transform (FFT) is the most efficiently known way to compute the Discrete Fourier Transform (DFT) of an arbitrary n-length signal, and has a computational complexity of O(n log n). If the DFT X of the signal x has only k…
Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic…
Let $\mathbb{F}_q$ be a finite field with $q$ elements and denote by $\theta : \mathbb{F}_q\to\mathbb{F}_q$ an automorphism of $\mathbb{F}_q$. In this paper, we deal with linear codes of $\mathbb{F}_q^n$ invariant under a semi-linear map…
Fractional repetition (FR) codes are a class of regenerating codes for distributed storage systems with an exact (table-based) repair process that is also uncoded, i.e., upon failure, a node is regenerated by simply downloading packets from…
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…
In this paper, several families of irreducible constacyclic codes over finite fields and their duals are studied. The weight distributions of these irreducible constacyclic codes and the parameters of their duals are settled. Several…
We focus on full-rate, fast-decodable space-time block codes (STBCs) for 2x2 and 4x2 multiple-input multiple-output (MIMO) transmission. We first derive conditions for reduced-complexity maximum-likelihood decoding, and apply them to a…
Recently proposed orthogonal time frequency space (OTFS) modulation has been considered as a promising candidate for accommodating various emerging communication and sensing applications in high-mobility environments. In this paper, we…