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cs.IT

cs.IT: explore 333 source-linked works published from 2021 to 2026, with original documents and citations.

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Includes records with this source-supplied label or an explicit phrase match in their metadata. Matches indicate a mention, not proof that a paper uses a method or tests a material. Source versions are consolidated by DOI.

Sources: arxiv. Collection updated 2026-09-16. Counts describe this index, not the complete source archives.

arXiv2025

The differential properties of certain permutation polynomials over finite fields

Finding functions, particularly permutations, with good differential properties has received a lot of attention due to their varied applications. For instance, in combinatorial design theory, a correspondence of perfect $c$-nonlinear functions and difference sets in some quasigroups was recently shown by Anbar et al. (J. Comb. Des. 31(12):1-24, 2023). Additionally, in a recent manuscript by Pal et al. (Adv. Math. Communications, to appear), a very interesting connection between the $c$-differential uniformity and boomerang uniformity, when $c=-1$, was pointed out, showing that they are the same for an odd APN permutation, sparking yet more interest in the construction of functions with low $c$-differential uniformity. We investigate the $c$-differential uniformity of some classes of permutation polynomials. As a result, we add four more classes of permutation polynomials to the family of functions that only contains a few (non-trivial) perfect $c$-nonlinear functions over finite fields of even characteristic. Moreover, we include a class of permutation polynomials with low $c$-differential uniformity over the field of characteristic~$3$. To solve the involved equations over finite fields, we use various number theoretical techniques, in particular, we find explicitly many Walsh transform coefficients and Weil sums that may be of an independent interest.

math.CO↗

arXiv2025

The revised boomerang connectivity tables and their connection to the Difference Distribution Table

It is well-known that functions over finite fields play a crucial role in designing substitution boxes (S-boxes) in modern block ciphers. In order to analyze the security of an S-box, recently, three new tables have been introduced: the Extended Boomerang Connectivity Table (EBCT), the Lower Boomerang Connectivity Table (LBCT), and the Upper Boomerang Connectivity Table (UBCT). In fact, these tables offer improved methods over the usual Boomerang Connectivity Table (BCT) for analyzing the security of S-boxes against boomerang-style attacks. Here, we put in context these new EBCT, LBCT, and UBCT concepts by connecting them to the DDT for a differentially $δ$-uniform function and also determine the EBCT, LBCT, and UBCT entries of three classes of differentially $4$-uniform power permutations, namely, Gold, Kasami and Bracken-Leander. We also determine the Double Boomerang Connectivity Table (DBCT) entries of the Gold function. As byproducts of our approach, we obtain some previously published results quite easily.

cs.CR↗

arXiv2024

3D Extended Target Sensing in ISAC: Cramér-Rao Bound Analysis and Beamforming Design

This paper investigates an integrated sensing and communication (ISAC) system where the sensing target is a three-dimensional (3D) extended target, for which multiple scatterers from the target surface can be resolved. We first introduce a second-order truncated Fourier series surface model for an arbitrarily-shaped 3D ET. Utilizing this model, we derive tractable Cramer-Rao bounds (CRBs) for estimating the ET kinematic parameters, including the center range, azimuth, elevation, and orientation. These CRBs depend explicitly on the transmit covariance matrix and ET shape. Then we formulate two transmit beamforming optimization problems for the base station (BS) to simultaneously support communication with multiple users and sensing of the 3D ET. The first minimizes the sensing CRB while ensuring a minimum signal-to-interference-plus-noise ratio (SINR) for each user, and it is solved using semidefinite relaxation. The second balances minimizing the CRB and maximizing communication rates through a weight factor, and is solved via successive convex approximation. To reduce the computational complexity, we further propose ISACBeam-GNN, a novel graph neural network-based beamforming method that employs a separate-then-integrate structure, learning communication and sensing (C&S) objectives independently before integrating them to balance C&S trade-offs. Simulation results show that the proposed beamforming designs that account for ET shapes significantly outperform existing baselines, offering better communication-sensing performance trade-offs as well as an improved beampattern for sensing. Results also demonstrate that ISACBeam-GNN is an efficient alternative to the optimization-based methods, with remarkable adaptability and scalability.

cs.IT↗

arXiv2023

The second-order zero differential spectra of some APN and other maps over finite fields

The Feistel Boomerang Connectivity Table and the related notion of $F$-Boomerang uniformity (also known as the second-order zero differential uniformity) has been recently introduced by Boukerrou et al.~\cite{Bouk}. These tools shall provide a major impetus in the analysis of the security of the Feistel network-based ciphers. In the same paper, a characterization of almost perfect nonlinear functions (APN) over fields of even characteristic in terms of second-order zero differential uniformity was also given. Here, we find a sufficient condition for an odd or even function over fields of odd characteristic to be an APN function, in terms of second-order zero differential uniformity. Moreover, we compute the second-order zero differential spectra of several APN or other low differential uniform functions, and show that our considered functions also have low second-order zero differential uniformity, though it may vary widely, unlike the case for even characteristic when it is always zero.

cs.IT↗

arXiv2023

Information geometric bound on general chemical reaction networks

We investigate the dynamics of chemical reaction networks (CRNs) with the goal of deriving an upper bound on their reaction rates. This task is challenging due to the nonlinear nature and discrete structure inherent in CRNs. To address this, we employ an information geometric approach, using the natural gradient, to develop a nonlinear system that yields an upper bound for CRN dynamics. We validate our approach through numerical simulations, demonstrating faster convergence in a specific class of CRNs. This class is characterized by the number of chemicals, the maximum value of stoichiometric coefficients of the chemical reactions, and the number of reactions. We also compare our method to a conventional approach, showing that the latter cannot provide an upper bound on reaction rates of CRNs. While our study focuses on CRNs, the ubiquity of hypergraphs in fields from natural sciences to engineering suggests that our method may find broader applications, including in information science.

physics.chem-ph↗

arXiv2023

High-dimensional Expansion of Product Codes is Stronger than Robust and Agreement Testability

We study the coboundary expansion property of product codes called product expansion, which played a key role in all recent constructions of good qLDPC codes. It was shown before that this property is equivalent to robust testability and agreement testability for products of two codes with linear distance. First, we show that robust testability for product of many codes with linear distance is equivalent to agreement testability. Second, we provide an example of product of three codes with linear distance which is robustly testable but not product expanding.

cs.IT↗

arXiv2023

Differential uniformity properties of some classes of permutation polynomials

The notion of $c$-differential uniformity has recently received a lot of attention since its proposal~\cite{Ellingsen}, and recently a characterization of perfect $c$-nonlinear functions in terms of difference sets in some quasigroups was obtained in~\cite{AMS22}. Independent of their applications as a measure for certain statistical biases, the construction of functions, especially permutations, with low $c$-differential uniformity is an interesting mathematical problem in this area, and recent work has focused heavily in this direction. We provide a few classes of permutation polynomials with low $c$-differential uniformity. The used technique involves handling various Weil sums, as well as analyzing some equations in finite fields, and we believe these can be of independent interest.

cs.IT↗

arXiv2022

Constructions of Polyphase Golay Complementary Arrays

Golay complementary matrices (GCM) have recently drawn considerable attentions owing to its potential applications in omnidirectional precoding. In this paper we generalize the GCM to multi-dimensional Golay complementary arrays (GCA) and propose new constructions of GCA pairs and GCA quads. These constructions are facilitated by introducing a set of identities over a commutative ring. We prove that a quaternary GCA pair is feasible if the product of the array sizes in all dimensions is a quaternary Golay number with an additional constraint on the factorization of the product. For the binary GCM quads, we conjecture that the feasible sizes are arbitrary, and verify for sizes within 78 $\times$ 78 and other less densely distributed sizes. For the quaternary GCM quads, all the positive integers within 1000 can be covered for the size in one dimension.

eess.SP↗

arXiv2021

Data-driven rational function neural networks: a new method for generating analytical models of rock physics

Seismic wave velocity of underground rock plays important role in detecting internal structure of the Earth. Rock physics models have long been the focus of predicting wave velocity. However, construction of a theoretical model requires careful physical considerations and mathematical derivations, which means a long research process. In addition, various complicated situations often occur in practice, which brings great difficulties to the application of theoretical models. On the other hand, there are many empirical formulas based on real data. These empirical models are often simple and easy to use, but may be not based on physical principles and lack a proper formulation of physics. This work proposed a rational function neural networks (RafNN) for data-driven rock physics modeling. Based on the observation data set, this method can deduce a velocity model which not only satisfies the actual data distribution, but also has a proper mathematical form reflecting the inherent rock physics. The Gassmann's equation, which is the most commonly used theoretical model relating bulk modulus of porous rock to mineral composition, porosity and fluid, is perfectly reconstructed by using data-driven RafNN. The advantage of this method is that only observational data sets are required to extract model equations, and no complex mathematical and physical processes are involved. This work opens up for the first time a new avenue on constructing analytical expression of velocity models using neural networks and field data, which is of great interest for exploring the heterogeneous structure of the Earth.

physics.geo-ph↗

Compare source metadata on this page

Work	Published	Source identifier	Source
The differential properties of certain permutation polynomials over finite fields	2025-01-27	2310.20205	arxiv
The revised boomerang connectivity tables and their connection to the Difference Distribution Table	2025-01-27	2407.12617	arxiv
3D Extended Target Sensing in ISAC: Cramér-Rao Bound Analysis and Beamforming Design	2024-12-24	2412.06353	arxiv
The second-order zero differential spectra of some APN and other maps over finite fields	2023-10-20	2310.13775	arxiv
Information geometric bound on general chemical reaction networks	2023-09-19	2309.10334	arxiv
High-dimensional Expansion of Product Codes is Stronger than Robust and Agreement Testability	2023-08-05	2308.02889	arxiv
Differential uniformity properties of some classes of permutation polynomials	2023-07-20	2212.01931	arxiv
Constructions of Polyphase Golay Complementary Arrays	2022-04-20	2204.09372	arxiv
Data-driven rational function neural networks: a new method for generating analytical models of rock physics	2021-09-18	2109.08813	arxiv

These are bibliographic comparisons, not experimental rankings. Follow the original document for methods and conditions.