21 papers · ranked by Valyu relevance
Hannes Bartz, Lukas Holzbaur, Hedongliang Liu, Sven Puchinger + 2 more
'Julian Renner' 'Antonia Wachter-Zeh'] The rank metric measures the distance between two matrices by the rank of their difference. Codes designed for the rank metric have attracted considerable attention in recent years, reinforced by network coding and further motivated by a variety of applications. In code-based…
Sanjit Bhowmick
A subspace code is a nonempty collection of subspaces of the vector space F n q . A pair of linear codes is called a linear complementary pair (in short LCP) of codes if their intersection is trivial and the sum of their dimensions equals the dimension of the ambient space. Equivalently, the two codes form an LCP if…
Dean Crnković, Andrea Švob
A subspace code is a nonempty set of subspaces of a vector space F n q . Linear codes with complementary duals, or LCD codes, are linear codes whose intersection with their duals is trivial. In this paper, we introduce a notion of LCD subspace codes. We show that the minimum distance decoding problem for an LCD…
Samin Riasat, Hessam Mahdavifar
Codes Authors: ['Samin Riasat' 'Hessam Mahdavifar'] Abstract—We propose efficient minimum-distance decoding and list-decoding algorithms for a certain class of analog subspace codes, referred to as character-polynomial (CP) codes, recently introduced by Soleymani and the second author. In particular, a CP code without…
Mladen Kovačević
Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than 1 are derived. An application in coding theory is illustrated by showing that multispace codes that are introduced here may be used in random linear network coding scenarios…
Ousmane Ndiaye, Peter Arnaud Kidoudou, Hervé Talé Kalachi
Rank-metric codes were studied by E. Gabidulin in 1985 after a brief introduction by Delsarte in 1978 as an equivalent of Reed-Solomon codes, but based on linearized polynomials. They have found applications in many areas, including linear network coding and spacetime coding. They are also used in cryptography to…
Han, Xiang, Xinran Li, Gang Wang
Flag codes are a class of multishot network codes comprising sequences of nested subspaces (flags) within the vector space F n q , where q is a prime power. In this paper, we propose a family of constructions for full flag codes based on partial spreads. The distances of this family include maximum distance (optimum…
Henk D. L. Hollmann, Patrick Solé
We construct a family of linear optimal functional-repair regenerating storage codes with parameters $({m,(n,k),(r,α,β)}={(2r-α+1)α/2,(r+1,r),(r,α,1)})$ for any integers $r,α$ with $1\leqα\leqr$, over any field when $α\in{1,r-1,r}$, and over any finite field $F_{q}$ with $q\geqr-1$ otherwise. These storage codes are…
William Dorrell, Peter E. Latham, Timothy E. J. Behrens, James C. R. Whittington
The efficient coding hypothesis presents a compelling success story for theoretical and systems neuroscience. It marshals a unifying idea, that neural codes can be understood as efficient encodings of natural stimuli, to explain phenomena from across sensory systems, sometimes with exquisite precision. However, similar…
Pablo T. Wentz, Scott L. Brincat, Anitha Pasupathy, Earl K. Miller
Cortical spiking activity in areas like prefrontal cortex (PFC) encodes information only along a small number of dimensions, a subspace of the full space of population activity patterns. PFC often uses distinct subspaces to represent incoming sensory information and to maintain it in working memory. However, it’s…
Wenjiao Xie, Huisheng Zhang, Yingjie Jay Guo
We propose a novel slot-pattern-control based coded compressed sensing for unsourced random access with an outer A-channel code capable of correcting t errors. Specifically, an RM extension code called patterned Reed-Muller (PRM) code is proposed. We demonstrate the high spectral efficiency due to its enormous sequence…
JeongJun Park, Charles D. Holmes, Lawrence H. Snyder
The prefrontal cortex (PFC) is crucial for maintaining working memory across diverse cognitive tasks, yet how it adapts to varying task demands remains unclear. Compositional theories propose that cognitive processes in neural network rely on shared components that can be reused to support different behaviors. However…
Francisco Revson F. Pereira, Stefano Mancini, Giuliano G. La Guardia
The Lindblad master equation describes the evolution of a large variety of open quantum systems. An important property of some open quantum systems is the existence of decoherence-free subspaces. A quantum state from a decoherence-free subspace will evolve unitarily. However, there is no procedural and optimal method…
Valéria G. Pedrosa, Max H. M. Costa, Sangun Park
The index coding problem consists of a system with a server and multiple receivers with different side information and demand sets, connected by a noiseless broadcast channel. The server knows the side information available to the receivers. The objective is to design an encoding scheme that enables all receivers to…
Eric Elmoznino, Michael F. Bonner
Geometric descriptions of deep neural networks (DNNs) have the potential to uncover core principles of computational models in neuroscience, while abstracting over the details of model architectures and training paradigms. Here we examined the geometry of DNN models of visual cortex by quantifying the latent…
Daniel Calabuig, Francisco J. González-Castaño
This paper analyzes the relationship between pilot symbol-assisted modulation (PSAM) and unitary space-time modulation (USTM). In particular, we present a map that transforms any PSAM into a USTM and vice versa. USTMs are known to be capacity-achieving. However, most of the proposed USTM construction methods in the…
Authors not listed
We present a comprehensive theoretical analysis of quantum subspace diagonalization methods for molecular electronic structure calculations, establishing rigorous complexity bounds and convergence guarantees. Building on recent developments in adaptive quantum algorithms for chemical systems, we formulate a general…
Beatriz Barbero-Lucas, Fernando Hernando, Helena Martín-Cruz, Gary McGuire
'Gary McGuire'] We construct new stabilizer quantum error-correcting codes from generalized monomial-Cartesian codes. Our construction uses an explicitly defined twist vector, and we present formulas for the minimum distance and dimension. Generalized monomial-Cartesian codes arise from polynomials in m variables. When…
Authors not listed
This work provides a rigorous theoretical investigation of selective error correction strategies for variational quantum algorithms, with focus on understanding the interplay between error suppression, circuit trainability, and computational resource requirements. We develop a mathematical framework that characterizes…
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The Hidden Subgroup Problem (HSP) unifies several landmark quantum algorithms, yet systematic exploration of its variants and modern applications has slowed. This paper revives HSP-based algorithm design by examining new group structures with direct relevance to post-quantum cryptography, lattice problems, and…
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The discovery of chemically novel or structurally anomalous metal-organic frameworks (MOFs) is essential for expanding reticular design space and enhancing dataset reliability. We present CHEM-AD (Chemically Unusual Metal–organic Frameworks via Autoencoder-based Detection), a label-free, CPU-efficient pipeline that…