A linear code is called t-divisible if every codeword has Hamming weight divisible by a fixed integer t. Such codes possess rich algebraic structure with important connections to combinatorics, geometry, and cryptography. In recent years, simplicial complexes have provided an effective framework for constructing t-divisible minimal and optimal codes. In this work, we study linear codes over & Rscr;= F2[u]/(u4-1) using simplicial complexes via the defining-set approach and analyze their binary Gray images. We construct binary t-divisible codes, establish conditions for minimality and self-orthogonality and obtain an infinite family of optimal codes meeting the Griesmer bound. As an application, we obtain several classes of binary locally recoverable codes of locality 2 and 3, and an infinite class of binary projective codes. Moreover, we explore the minimal access structures of a secret-sharing schemes based on the duals of these binary minimal codes. Finally, we construct several classes of strongly regular Cayley graphs from binary projective 2-weight codes and determine their parameters. We also show that their complement graphs are strongly regular and obtain their corresponding parameters. (c) 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Software Defined Networking (SDN) and Network Function Virtualization (NFV) are expected to provide greater flexibility and manageability for next-generation IoT networks. In this context, network services should be modeled as Virtual Network Function Forwarding Graphs (VNF-FGs). A key challenge is efficient allocation of resources for sequentially arriving network service requests, a process known as VNF-FG placement. Most existing algorithms either manually or partially extract features from the physical network and VNF-FG or adopt a greedy approach, allocating resources as long as a feasible solution exists, which may over-allocate resources to VNF-FG requests, ultimately harming infrastructure providers’ long-term revenue. In this paper, we propose a VNF-FG placement and admission control algorithm based on hierarchical reinforcement learning, called EAC. It consists two levels of agents: a coarse-level agent that generates placement strategies and rejects requests with no feasible placement strategies, and a refine-level agent that implements admission control and rejects requests that are detrimental to long-term revenue. To fully capture the topological features of both the physical network and the VNF-FG, we employ a customized Graph Attention Network (GAT) that incorporates link feature awareness and enables deeper exploration. To fully explore historical temporal information for admission control, we construct state triples and feed them into a Recurrent Neural Network (RNN). Using Proximal Policy Optimization (PPO) as the foundational training algorithm, the corresponding agents are trained hierarchically. Extensive experimental results demonstrate that the proposed EAC algorithm outperforms existing state-of-the-art solutions in terms of acceptance rate, revenue-to-cost ratio, and long-term average revenue.

Fractional ambiguity functions consider fractional Doppler shifts and are crucial for channel estimation in high-speed scenarios. Generalized chirp-like (GCL) sequences are well-known in communication systems because of their favorable correlation properties. In this paper, using the properties of incomplete exponential sums, we analyze the fractional ambiguity functions of two types of GCL sequences: one constructed using cyclically shifted Zadoff-Chu sequences, and the other based on DFT matrices. Further, based on the rational number reconstruction, we find a sequence set with low ambiguity zone.

Due to constraints in network capacity and coverage, conventional ground-based infrastructures face difficulties in delivering low-latency and high-reliability caching capabilities to users and Internet of Things (IoT) devices located in remote regions, including mountains and oceans. The Space-Air-Ground Integrated Network (SAGIN), envisioned as a foundational structure for 6G communication systems and integrated with Mobile Edge Computing (MEC), can offer a promising solution to efficiently serve the caching demands of users in such underserved locations. Nevertheless, the high heterogeneity and time-varying nature of SAGIN, along with the continuous evolution of the popularity of user requested content, which presents substantial challenges to achieve satisfactory cache hit ratios and low access latency. In this paper, we introduce a novel three-tier edge collaborative caching architecture comprising satellites, Unmanned Aerial Vehicle (UAV) clusters, and ground edge servers. We formulate the cache replacement task as a Markov Decision Process (MDP). To address concerns over user privacy and heterogeneous local model performance, we propose a Federated Discrete Soft Actor-Critic (FDSAC) approach that employs an attention mechanism guided by server activity levels to adaptively weight client models during parameters aggregation. Additionally, a content popularity prediction module based on Bidirectional Long Short-Term Memory (BiLSTM) is embedded within the DSAC agent to derive the optimal cache replacement decisions. Experimental evaluations indicate that the FDSAC achieves superior performance compared to other baseline algorithms in terms of both cache hit rate and content retrieval delay.

Quasi-complementary sequence sets (QCSSs) play a vital role in multi-carrier code-division multiple-access (MC-CDMA) systems. Compared to perfect complementary sequence sets (PCSSs), QCSSs can support a larger number of communication users. In this work, we propose a novel construction of QCSSs by leveraging specific one-coincidence frequency-hopping sequence sets (OC-FHSSs), which enables the generation of previously unattainable parameters. Importantly, the proposed QCSSs are asymptotically optimal with respect to the Liu–Guan–Ng–Chen bound.

Low ambiguity zone (LAZ) sequences play a crucial role in modern integrated sensing and communication (ISAC) systems. In this paper, we introduce a novel class of functions known as locally perfect nonlinear functions (LPNFs). By utilizing LPNFs and interleaving techniques, we propose three new classes of both periodic and aperiodic LAZ sequence sets with flexible parameters. The proposed periodic and aperiodic LAZ sequence sets are asymptotically optimal with respect to the periodic and aperiodic lower AF bounds, respectively, which were proposed recently in [IEEE J. Sel. Areas Commun. 40 (6): 1809-1822]. Notably, the aperiodic LAZ sequence sets are the first such sequence sets in the literature that satisfy the bound. Finally, we demonstrate that the proposed sequence sets are cyclically distinct.

The dual-function radar-communication (DFRC) network has emerged as a pivotal solution for integrating radar sensing and wireless communication within a unified platform, significantly improving spectral efficiency and hardware utilization. This field has evolved from basic DFRC architectures to more sophisticated frequency-hopping multiple-input multiple-output (FH-MIMO) DFRC networks. Such networks leverage frequency agility and spatial diversity to substantially enhance resilience against interference and increase the achievable communication data rate. However, fixed frequency-hopping patterns assigned to each transmit antenna restrict the independent and flexible optimization of resources across the spatial and frequency domains. In this paper, we introduce a novel waveform structure that incorporates generalized spatial modulation (GSM) into the FH-MIMO DFRC network. The proposed GSM-FH-MIMO DFRC facilitates a more efficient and dynamic utilization of the available time, frequency, and spatial resources. Communication information is intelligently embedded through a synergistic combination of FH codes, phase modulation, and the activation states (indices) of transmit antennas, thereby creating a multi-dimensional modulation scheme. For information decoding at the communication receiver, a method based on the discrete Fourier transform (DFT) is developed. Furthermore, we present a rigorous analysis of the achievable data transmission rates under different system configurations and derive the optimal number of active antennas to maximize overall network efficiency. Simulation results verify that the proposed GSM-FH-MIMO DFRC network significantly enhances the communication data rate without degrading radar functionality. Moreover, in certain scenarios, the proposed waveform also yields advantages in terms of radar waveform ambiguity and target detection performance.

Integrated sensing and communications (ISAC) is revolutionizing low-altitude wireless networks (LAWN), making them vital for next-generation communication systems. However, effectively suppressing interference while balancing critical sensing tasks in multi-user multiple-input multiple-output (MU-MIMO) orthogonal frequency division multiplexing (OFDM) architectures remains a formidable challenge. By leveraging the spatial degrees of freedom (DoFs) in multi-antenna systems, this study presents an innovative transceiver beamforming design for MU-MIMO OFDM ISAC systems that effectively suppresses interference and optimizes beampattern sidelobes, significantly enhancing system efficiency. Specifically, we formulate a joint optimization problem to maximize the communication weighted sum rate subject to constraints on transmit power, the sensing signal-to-clutter-plus-noise ratio (SCNR), the peak sidelobe level (PSL) of the transmit beampattern, and spatial nulling requirements. To tackle the resulting NP-hard non-convex problem, we first transform it into an equivalent convex weighted minimum mean-square error (WMMSE) problem and develop an efficient alternating optimization algorithm based on successive convex approximation (SCA). Extensive simulation results demonstrate the effectiveness of the proposed scheme in efficiently suppressing interference and optimizing the beampattern, thereby confirming the efficacy of the proposed algorithm and paving the way for more reliable and efficient LAWN.

Dual-rectangular zero ambiguity zone (ZAZ) sequence sets play an important role in multi-mode integrated sensing and communication (ISAC) systems. In this paper, we propose two classes of dual-rectangular ZAZ sequence sets. Specifically, we first construct a class of dual-rectangular ZAZ sequence sets based on novel exponential functions. We then develop a general construction framework for dual-rectangular ZAZ sequence sets via the interleaving technique. All the proposed constructions are proven to be asymptotically optimal with respect to the Ye-Zhou-Fan-Liu-Lei-Tang (YZFLLT) bounds under the corresponding asymptotic condition.

This paper presents a RIS-assisted full-duplex (FD) integrated sensing and communication (ISAC) system designed to enhance communication and radar functions simultaneously. We propose an optimization framework that maximizes power efficiency while satisfying the signal-to-interference-plus-noiseratio (SINR) requirements for both uplink/downlink (UL/DL) and radar signals. The challenge arises due to the numerous interrelated optimization variables involved. To solve this nonconvex problem, we introduce an alternating optimization (AO) algorithm utilizing successive convex approximation (SCA) and penalty function (PF) methods. Numerical results validate the effectiveness of our proposed algorithm and demonstrate the advantages of the RIS-assisted FD-ISAC scheme.

Space-Air-Ground Integrated Network (SAGIN) is a key architecture for achieving wide-area sensing and communication services. However, the connection between Low Earth Orbit (LEO) satellites and ground devices is constrained by satellite mobility and service angles. Unmanned Aerial Vehicles (UAVs), acting as relay and sensing nodes, can effectively bridge this gap. Nevertheless, under their limited onboard resources, the coupled impacts between UAV trajectory planning and the performance of communication and sensing-especially in scenarios where multi-UAV collaboration extends LEO service coverage-have not been fully investigated. To address these challenges, this paper proposes an integrated sensing and computation offloading architecture for SAGIN, where UAVs perform multi-target sensing while cooperating with LEO satellites to provide communication and computational services. We formulate a joint optimization problem that encompasses user offloading decisions, communication-sensing time allocation, UAV trajectory planning, and computing resource allocation, aiming to minimize long-term service latency. This problem is modeled as a mixed-integer nonlinear program (MINLP). To efficiently solve it, we develop a low-complexity Lyapunov-Benders Optimization (LBO) algorithm based on Lyapunov optimization and generalized Benders decomposition, which decomposes the long-term problem into tractable single-slot subproblems. Simulation results validate that the proposed method outperforms existing benchmarks in service latency, demonstrating its effectiveness in dynamic SAGIN environments.

Arrays with good correlation properties have emerged with promising applications in wireless communication, including ultra-wideband (UWB), two-dimensional (2- D) synchronization, and massive multiple-input multiple-output (MIMO). In this paper, we propose two efficient algorithms for designing arrays with low autocorrelation by minimizing the weighted integrated sidelobe level (WISL) and complementary ISL (CISL), respectively. We formulate these metrics as non-convex quartic problems under unimodular constraints in the frequency domain. Using the majorization-minimization (MM) framework, these problems are simplified into quadratic forms, ensuring monotonic convergence to a stationary point. Furthermore, a projection algorithm is introduced to relax unimodular constraints to peak-to-average power ratio (PAPR) constraints, enhancing the correlation performance of the optimized arrays. All proposed algorithms can be efficiently implemented using two-dimensional FFT/IFFT operations. Furthermore, a quasi-complementary array set (QCAS), generated via the proposed MM-ACISL algorithm, is applied as an omnidirectional precoding matrix in massive MIMO systems. Numerical experiments demonstrate that the proposed algorithms outperform existing methods in terms of both correlation performance and computational efficiency. Moreover, the resulting QCAS scheme effectively enables omnidirectional transmission in MIMO systems.

Sequences with excellent ambiguity functions are very useful in radar detection and modern mobile communications. Doppler resilient complementary sequence (DRCS) is a new type of sequence proposed recently, which can achieve lower ambiguity function sidelobes by summing the ambiguity functions of subsequences. In this paper, we introduce some new constructions of DRCS sets (DRCSSs) based on one-coincidence frequency-hopping sequence sets (OC-FHSSs), almost difference sets (ADSs) and Z-complementary code sets (ZCCSs). Critically, the proposed DRCSSs are optimal or near optimal.

Within the zero-correlation-zone (ZCZ), ZCZ sequence sets exhibit ideal correlation properties, which is highly advantageous for both wireless communications and radar sensing applications. Recently, to achieve optimal training for spatial modulation (SM), Pai et al. introduced the concept of sparse ZCZ (SZCZ) sequence sets, where each column contains only one non-zero element. In this paper, we first extend the SZCZ sequence set concept by permitting multiple non-zero elements per column, thereby accommodating training design requirements for generalized SM (GSM) systems. Then, we propose a direct construction of SZCZ sequence sets with parameter (q(n+k),q(m+n+k),(q-1)q(pi(2)-1)+(q-2)q(pi(3)-1),(q(n),q(m+n))) based on restricted extended Boolean functions. Compared to existing works, the proposed SZCZ sequence sets exhibit a greater ZCZ width and can be applied to both SM and GSM training designs simultaneously. Simulation results show that compared with other training sequences, the channel estimation performance is significantly improved when the proposed SZCZ sequence set is used as the training sequences.

Z-complementary code sets (ZCCSs) are widely used in multi-carrier code-division multiple access (MC-CDMA) and multiple-input multiple-output (MIMO) communication due to their excellent correlation properties within a specific region around the in-phase position known as the zero correlation zone (ZCZ). In this paper, we introduce the concept of a partially m-shifted orthogonal complementary code, and use it to construct optimal ZCCSs by combining complete complementary codes (CCCs). The resulting optimal ZCCSs are not covered by existing literature.

Owing to their zero aperiodic correlation sum properties, complete complementary codes (CCCs) have an important application in asynchronous multi-carrier code division multiple access (MC-CDMA) systems, whereby the peak-to-average-power ratio (PAPR) is determined by the column sequences of complementary matrices. Inspired by this, a new class of (q^k,q^m) -CCCs with column sequence PAPR of at most q is developed based on extended Boolean functions. The effectiveness of the proposed CCCs is validated by showing improved bit error performance in frequency selective channels.

Sequences play an important role in communication and radar systems, where related theoretical bounds serve as benchmarks to access the designed sequences. This paper first studies the odd-periodic ambiguity function (OPAF) of sequence sets and derives a theoretical lower bound of its magnitude. Based on the even-odd transformation, the relationship between the periodic ambiguity function and the odd-periodic ambiguity function is established. Furthermore, we construct two classes of odd-periodic sequences that achieve the optimal zero ambiguity zone (ZAZ) by leveraging the properties of known sequences and quadratic functions. Finally, we present a class of low ambiguity zone (LAZ) sequence sets by using certain cubic functions, which is asymptotically optimal with respect to the derived bound.

Sequences with excellent ambiguity functions are very useful in radar detection and modern mobile communications. Doppler resilient complementary sequence (DRCS) is a new type of sequence proposed recently, which can achieve lower ambiguity function sidelobes by summing the ambiguity functions of subsequences. In this paper, we introduce some new constructions of DRCS sets (DRCSSs) based on one-coincidence frequency-hopping sequence sets (OC-FHSSs), almost difference sets (ADSs), some specific sequences, etc. Critically, the proposed DRCSSs are optimal or near optimal.

Binary sequences are of vital importance in the fields of communication and cryptography. This paper delves into the design of binary sequences for Ambient-powered (AMP) synchronization fields within the context of the Internet of Things (IoT). In our study, we first define the novel aperiodic autocorrelation functions tailored to the AMP scenario. A new metric for aperiodic correlation is proposed, which takes into consideration the data structure of Manchester encoding. By integrating the genetic algorithm, we efficiently search for some optimal binary sequences. Experimental results show that the sequence obtained by this new metric exhibit better performance compared to classical sequences.