Efficient task allocation among multiple UAVs and autonomous robots is critical in modern IoT scenarios. This is typically modeled as a multi-robot task allocation (MRTA) problem, known to be an NP-hard combinatorial optimization problem. Neural sequential modeling combined with reinforcement learning (RL) optimization has emerged as a promising paradigm for solving this problem, owing to its high efficiency during inference. However, most existing methods assume that each robot is capable of performing only a single type of task. The development of sensing technologies has significantly enhanced the functional diversity of robots, thereby challenging the effectiveness and scalability of traditional methods. This paper considers a variant of the MRTA problem, where each robot is capable of handling multiple tasks, and tasks vary in both their types and required resources. To this end, we present a novel game-theoretic multi-agent RL algorithm called multi-agent policy gradient via potential game (MAPG2). The key components of proposed method consist of three parts. Firstly, we utilize graph-based attention model (GAM) to characterize the representations between tasks. Secondly, we formulate the single-step allocation process as a potential game (PG) to guarantee the consistency and soundness of the reward function design. Lastly, our approach sequentially generates allocation strategies through centralized training and decentralized execution (CTDE) framework. Extensive experiments demonstrate that MAPG2achieves a 10% improvement in task completion rate compared to state-of-the-art baselines, validating its effectiveness and robustness.

With the accelerated development of large models and distributed training, the explosive growth of data volume has brought huge challenges to traditional data processing and machine learning algorithms. The inconsistency and accuracy of the data processing process will directly affect the analysis and decision-making effect of the data. In this paper, we investigate a data fusion framework based on a trustworthiness metric model, aiming to incorporate a credibility evaluation mechanism of data sources into the data fusion process. Firstly, we propose a trust measurement model based on dynamic Bayesian networks that is correlated with time factors, taking into account the impact of network interaction behavior on trust measurement. Secondly, we design a data security aggregation mechanism based on the trustworthy measurement model, which combines credibility measurement with the minimum spanning tree (MST) protocol to improve the network's perception performance. Finally, we conduct simulation experiments and real experimental bed tests separately, and the results showed that the proposed model has continuous trustworthiness measurement ability in dynamic uncertain network environments. On a large benchmark dataset, the proposed algorithm performs better than state-of-the-art methods in statistics, with a significant reduction rate of 36.6% in the computational cost of the control center, and a reduction rate of 23.8% and 34.7% in the communication and storage costs of the system, respectively.

Solomon-Stiffler codes and Belov codes are two wellknown families of Griesmer codes that have recently attracted significant attention in recent coding-theoretic literature, due to their optimality and special algebraic structures. In this paper, we investigate their subfield codes and hull dimensions. Firstly, we establish the parameters of Solomon-Stiffler and Belov codes by means of exponential sums. Following the approach of Hyun et al. (IEEE Trans. Inf. Theory, 71(6): 4267-4283, 2025), we determine the exact parameters of the subfield codes of Solomon-Stiffler codes and Belov codes; for the non-projective case, the parameters are fixed, while for the projective case, they depend on the number of distinct types of generator matrices of the mutually disjoint subspaces. We also derive an explicit formula for the weight enumerators of Solomon-Stiffler codes. Secondly, we characterize the hull dimensions of Solomon-Stiffler codes and Belov codes, thereby extending the results of Shi et al. (J. Combin. Theory, Ser. A, 214: 106027, 2025) on the self-orthogonality of binary Solomon-Stiffler codes and Belov codes. As a consequence, we also obtain several families of self-orthogonal codes.

In this paper, we mainly investigate profound interconnections between combinatorial designs, linear codes, and Boolean functions. Firstly, we present a generic construction method for designs derived from Boolean functions and give a new concept of non-symmetric designs with the triple symmetric difference property (TSDP). Secondly, we provides an alternative proof for addition designs derived from plateaued functions, which need not be simple or symmetric. We characterize simple 2-designs on 2m−rpoints arising fromr-plateaued functions inmvariables, and show that addition designs from such functions with no nonzero linear structure satisfy the TSDP but not the double one, yielding non-symmetric simple 2-designs. Thirdly, we primarily explore the equivalence relationships between designs, linear codes, and plateaued functions. These investigations help resolve two open problems posed by Ding and Tang (Designs from Linear codes, Singapore: World Scientific, 2022: Problems 14.20, 14.23).We also compute the automorphism groups of addition designs ofr-plateaued functions and of the linear codes of addition designs. This work extends results by Bending (SDP designs and their automorphism groups, Ph.D. thesis, 1993), and Dempwolff and Neumann (Des. Codes Cryptogr., 57, 373–381, 2010). Finally, we yield new Boolean functions producing two families of a 2-design whose parameters coincide with those of the complement of a point-hyperplane design and a TSDP design, despite being non-isomorphic.

The seizure early warning devices based on multichannel EEG signals is one of the most used assisted-living strategies for drug-resistant epileptic patients. One of the challenges in the development of these devices is that existing algorithms cannot avoid the effects of electrode loosening. To alleviate such problem, a seizure prediction model robust to corrupted EEG recordings is proposed in this paper. This method intends to learn a stable feature space adapted to different corruption versions via constructing a jointly-optimized autoencoder. Robust information is captured during the reconstruction process by developing a corruption module, while an adversarial training procedure circumvents overfitting using variational inference. Moreover, a regularization term is designed to minimize the distance among various corruption versions in the embedding space with the Riemannian manifold-based distribution alignment. Both raw EEG data and corrupted EEG data are utilized to evaluate prediction performance. Experimental results indicate that this method can predict seizures effectively and stably under the condition of electrode looseness.

Customer-generated reviews on e-commerce websites often contain valuable insights into users' interests in product genres and provide a rich source for mining user preferences. However, most existing neural topic models tend to generate meaningless topics that share low correlations with product genres. Furthermore, they often fail to mine user preferences and discover personalized topic profiles due to the absence of explicit user modeling. To address these limitations, we propose a novel Genre-aware Personalized neural Topic Model (GPTM), which incorporates product genre information into the topic modeling process to ensure the relevance between mined topics and product genres. Moreover, it could produce a personalized topic profile for each user by performing user preference modeling. Extensive experimental results on three publicly available Amazon review corpora validate the effectiveness of the proposed GPTM in genre-aware topic modeling. Furthermore, GPTM surpasses state-of-the-art baselines in user preference mining and generates high-quality personalized topic profiles.

The primary objective of this paper is the construction of optimal codes with self-orthogonality that can be used to construct quantum codes. Recently, Ding and Heng explored subfield codes, which can be viewed as trace codes. In this paper, we focus on investigating self-orthogonal optimal trace codes. First, we provide a novel description of trace codes by choosing suitable defining sets. Second, we determine the parameters of the codes and their trace codes whose defining sets are disjoint union of some affine subspaces in both non-projective cases and projective-cases. This result extends the main findings in (Hu, Li, Zeng, Wang, Tang, IEEE Trans. Inform. Theory, 68(7): 4408-4421, 2022). Third, we compute the parameters of trace codes for MacDonald codes, including the first order Reed-Muller codes and simplex codes as special cases. Finally, we examine their self-orthogonality and distance-optimality to find several classes of self-orthogonal Griesmer codes. Additionally, we resolve a problem proposed by Ding and Heng as a byproduct.

The storage and transmission of large-scale data are recognized as significant challenges that incur substantial costs due to the massive volume of information involved. Lossless compression offers a potential solution to this problem. In this work, we explore the online lossless state compression (LSC) in finite-valued networks by effectively combining the methods of finite state automata and reinforcement learning. To achieve online lossless compression, the concept ofk-step compressed walks (state sequences) is introduced. By constructing a finite state automaton to identify all insertable walks, the recoverability conditions of online lossless compression are presented. For any given compressed walkw’c, one algorithm is proposed to find a minimal recoverablekmin-step compressed walk, thereby improving the compression ratio. Furthermore, it can be found that if a compressed walk keeps recoverability, adding more states to it would not break this property. Additionally, a model-free reinforcement learning framework based on Q-learning is developed to obtain globally minimal recoverable compressed walks. Finally, a numerical example is given to demonstrate the efficiency of the proposed online lossless compression scheme, achieving a compression ratio of 44.4%.

For a given linear code$\mathcal {C}$of length n over${\mathrm {GF}}(q)$and a nonzero vector u in${\mathrm {GF}}(q)^{n}$, Sun, Ding and Chen defined an extended linear code$\overline {\mathcal {C}}({\mathbf {u}})$of$\mathcal {C}$, which is a generalisation of the classical extended code$\overline {\mathcal {C}}(-{\mathbf {1}})$of$\mathcal {C}$and called the second kind of an extended code of$\mathcal {C}$(see Finite Fields Appl., vol. 96, 102401, 2024 and Discrete Math., vol. 347, no. 9, 114080, 2024). They developed some general theory of the extended codes$\overline {\mathcal {C}}({\mathbf {u}})$and studied the extended codes$\overline {\mathcal {C}}({\mathbf {u}})$of several families of linear codes, including cyclic codes, projective two-weight codes, nonbinary Hamming codes, and a family of reversible MDS cyclic codes. The objective of this paper is to investigate the extended codes$\overline {\mathcal {C}}({\mathbf {u}})$of MDS codes$\mathcal {C}$over finite fields. The main result of this paper is that the extended code$\overline {\mathcal {C}}({\mathbf {u}})$of an MDS$[n,k]$code$\mathcal {C}$remains MDS if and only if the covering radius$\rho (\mathcal {C}^{\bot })=k$and the vector u is a deep hole of the dual code${\mathcal {C}}^{\perp } $. As applications of this main result, an equivalent statement of MDS Conjecture is presented, the extended codes of the GRS codes and extended GRS codes are investigated, and the covering radii and some deep holes of several families of MDS codes are also determined.

Linear codes are widely studied in coding theory as they have nice applications in distributed storage, combinatorics, lattices, cryptography and so on. Constructing linear codes with desirable properties is an interesting research topic. In this paper, based on the augmentation technique, we present two families of linear codes from some functions over finite fields. The first family of linear codes is constructed from monomial functions over finite fields. The weight distribution of the codes is determined in some cases. The codes are proved to be both optimally or almost optimally extendable and self-orthogonal under certain conditions. The localities of the codes and their duals are also studied and we obtain an infinite family of optimal or almost optimal locally recoverable codes. The second family of linear codes is constructed from weakly regular bent functions over finite fields and its weight distribution is explicitly determined. This family of codes is also proved to be both optimally or almost optimally extendable and self-orthogonal. Besides, this family of codes has been proven to have locality 2 or 3 under certain conditions. Particularly, we derive two infinite families of optimal locally recoverable codes. Some infinite families of 2-designs are obtained from the codes in this paper as byproducts.

BCH codes and their dual codes are two special subclasses of cyclic codes and are the best linear codes in many cases. A lot of progress on the study of BCH cyclic codes has been made, but little is known about the minimum distances of duals of BCH codes. Recently, a concept called dually-BCH code was introduced to investigate the duals of BCH codes and the lower bounds on their minimum distances in Gong et al., (2022). For a prime power$q$and an integer$m \ge 4$, let$n=\frac {q^{m}-1}{q+1}$($m$even), or$n=\frac {q^{m}-1}{q-1}$($q>2$). In this paper, some sufficient and necessary conditions in terms of the designed distance will be given to ensure that the narrow-sense BCH codes of length$n$are dually-BCH codes, which extended the results in Gong et al., (2022). Lower bounds on the minimum distances of their dual codes are developed for$n=\frac {q^{m}-1}{q+1}$($m$even). As byproducts, we present the largest coset leader$\delta _{1}$modulo$n$being of two types, which proves a conjecture in Wu et al., (2019) and partially solves an open problem in Li et al., (2017). We also investigate the parameters of narrow-sense BCH codes of length$n$with design distance$\delta _{1}$. The BCH codes presented in this paper have good parameters in general.

Recently, Hyun et al. have utilized simplicial complexes to construct several infinite families of binary minimal and optimal linear codes. Building upon their work, we draw inspiration and extend their research by constructing codes over the ring$\mathbb {Z}_{4}$with the aid of simplicial complexes. In this paper, we present two infinite families of quaternary codes, one of which is linear while the other is nonlinear. We analyze the Lee weight distributions of the resulting quaternary codes and compare them with the existing database of$\mathbb {Z}_{4}$codes. Our findings reveal the discovery of several new quaternary codes. Furthermore, we also provide two classes of binary codes that can be obtained from these quaternary codes using the Gray map.

Recently, simplicial complexes are used in constructions of several infinite families of minimal and optimal linear codes by Hyunet al. Building upon their research, in this paper more linear codes over the ring Z4are constructed by simplicial complexes. Specifically, the Lee weight distributions of the resulting quaternary codes are determined and two infinite families of four-Lee-weight quaternary codes are obtained. Compared to the databases of Z4codes by Aydinet al., at least nine new quaternary codes are found. Thanks to the special structure of the defining sets, we have the ability to determine whether the Gray images of certain obtained quaternary codes are linear or not. This allows us to obtain two infinite families of binary nonlinear codes and one infinite family of binary minimal linear codes. Furthermore, utilizing these minimal binary codes, some secret sharing schemes as a byproduct also are established.

Cyclic codes are important in theory, as they are closely related to a number of areas of mathematics. Cyclic codes are also important in practice, as they have efficient encoding and decoding algorithms. An infinite family of cyclic codes over GF(q) is said to have linearly-best-known parameters if for any [n,k,d] codeCin this family, there is no known [n,k,d′] linear code over GF(q) such thatd′ >d. An infinite family of cyclic codes over GF(q) is said to have cyclicly-best-known parameters if for any [n,k,d] codeCin this family, there is no known [n,k,d′] cyclic code over GF(q) such thatd′ >d. It is very rare to see an infinite family of binary cyclic codes with cyclicly-best-known parameters whose duals codes have also cyclicly-best-known parameters. The objective of this paper is to study such family of binary cyclic codes of length 2m– 1 and dimension 2m– 1 –m(m– 1)/2, denoted byC(2,m,2), and their dual codesC⊥(2,m,2). The weight distribution ofC⊥(2,m,2)is settled and the parameters ofC(2,m,2)are investigated in this paper. A larger family of binary cyclic codesC(2,m,r)and their duals are also constructed and studied in this paper, where 0 ≤r≤m– 1.

In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and defining sets. Second, we construct quaternary linear codes via simplicial complexes and determine the weight distributions of these codes. Third, the weight distributions of the binary subfield codes of these quaternary codes are also computed by employing the general characterization. Furthermore, we present two infinite families of optimal linear codes with respect to the Griesmer Bound, and a class of binary almost optimal codes with respect to the Sphere Packing Bound. We also need to emphasize that we obtain at least 9 new quaternary linear codes.

Both linear complementary dual (LCD) codes and maximum distance separable (MDS) codes have good algebraic structures, and they have interesting practical applications such as communication systems, data storage, quantum codes, and so on. So far, most of LCD MDS codes have been constructed by employing generalized Reed-Solomon codes. In this paper we construct some classes of new Euclidean LCD MDS codes and Hermitian LCD MDS codes which are not monomially equivalent to Reed-Solomon codes, called LCD MDS codes of non-Reed-Solomon type. Our method is based on the constructions of Beelen et al. (2017) and Roth and Lempel (1989). To the best of our knowledge, this is the first paper on the construction of LCD MDS codes of non-Reed-Solomon type; any LCD MDS code of non-Reed-Solomon type constructed by our method is not monomially equivalent to any LCD code constructed by the method of Carlet et al. (2018).

Let Fqbe a finite field with q elements and p be a prime with gcd(p, q) = 1. Let G be a finite abelian p-group and Fq(G) be a group algebra. In this paper, we find all primitive idempotents and minimal abelian group codes in the group algebra Fq(G). Furthermore, we give all LCD abelian codes (linear code with complementary dual) and self-orthogonal abelian codes of Fq(G).

Recently, some infinite families of binary minimal and optimal linear codes were constructed from simplicial complexes by Hyun et al. Inspired by their work, we present two new constructions of codes over the ring F2+ uF2by employing simplicial complexes. When the simplicial complexes are all generated by a maximal element, we determine the Lee weight distributions of two classes of the codes over F2+ uF2. Our results show that the codes have few Lee weights. Via the Gray map, we obtain an infinite family of binary codes meeting the Griesmer bound and a class of binary distance optimal codes.

Constacyclic codes are well-known generalizations of cyclic and negacyclic codes. Due to their rich algebraic structure, constacyclic codes are used to construct quantum codes and symbol-pair codes. Let${\mathbb {F}}_{q}$be a finite field with order$q$, where$q$is a positive power of a prime$p$. Suppose that$n$is a positive integer and the product of distinct prime factors of$n$divides$q-1$, i.e.,$rad(n)\mid (q-1)$. In this paper, we explicitly factorize the polynomial$x^{n}-\lambda $for each$\lambda \in {\mathbb {F}}_{q}^{*}$. As applications, first, we obtain all repeated-root$\lambda $-constacyclic codes and their dual codes of length$np^{s}$over${\mathbb {F}}_{q}$; second, we determine all simple-root LCD cyclic codes and LCD negacyclic codes of length$n$over${\mathbb {F}}_{q}$; third, we list all self-dual repeated-root negacyclic codes of length$np^{s}$over${\mathbb {F}}_{q}$. In contrast to known results, the lengths of constacyclic codes in this paper have more flexible parameters.

Let$\Bbb F_{p}$be a finite field with$p$elements, where$p$is a prime. Let$N \ge 2$be an integer and$d$be the least positive integer satisfying$p^{d} \equiv -1 \pmod N$. Let$q = p^{2sd}$for some integers$s$. In some special cases, we obtain the explicit evaluation of the following exponential sums:$S(a,b)=\sum _{x\in \Bbb F_{q}^{*}}\zeta _{p}^{ \mathrm {Tr}_{q/p}(ax^{(({q-1})/{N})}+bx)}$. As applications, Walsh spectrums of the monomial functions$\mathrm {Tr}_{q/p}(x^{(({q-1})/{N})})$in three cases are investigated. Our results show that Walsh spectrums of the monomial functions have at most four, five, or seven distinct values. Furthermore, three families of the monomial functions with three-valued Walsh spectrums are presented, seeCorollaries 12,21,31, and32. Consequently, certain previously known results by Li and Yue and Moisio are extended.