Abstract Named entity recognition (NER) is a fundamental task for natural language processing, which aims to detect mentions of real-world entities from text and classifying them into predefined types. Recently, research on overlapped and discontinuous named entity recognition has received increasing attention. However, we note that few studies have considered both overlapped and discontinuous entities. In this paper, we proposed a novel sequence-to-sequence model that is capable of recognizing both overlapped and discontinuous entities based on machine reading comprehension. The model utilizes machine reading comprehension formulation to encode significant inferior information about the entity category. Then input sequence passes through a question-answering model to predict the mention relevance of the given source sentences to the query. Finally, we incorporate the mention relevance into the BART-based generation model. We conducted experiments on three type of NER datasets to show the generality of our model. The experimental results demonstrate that our model beats almost all the current top-performing baselines achieves a vast amount of performance boost over current SOTA models on overlapped and discontinuous NER datasets.

Abstract: Constant dimension codes (CDCs), as special subspace codes, have received a lot of attention due to their application in random network coding. This paper introduces a family of new codes, called Ferrers diagram rank-metric codes with given ranks (GFRMCs), to generalize the parallel construction and the parallel multilevel construction in [IEEE Trans. Inf. Theory, 66 (2020), 6884–6897]. The lower bounds for GFRMCs are derived from Ferrers diagram rank-metric codes (FDRMCs). Via GFRMCs, the inverse multilevel construction for CDCs is showed. Furthermore, the double multilevel construction, as an effective construction for CDCs, is presented by combining the inverse multilevel construction and the multilevel construction. Many CDCs with larger size than the previously best known codes are given.

Optical orthogonal signature pattern codes (OOSPCs) have played an important role in a novel type of optical code-division multiple-access network for 2-D image transmission. In this paper, we give four direct constructions for OOSPCs based on polynomials and rational functions over finite fields. We also use r -simple matrices to present a recursive construction for OOSPCs. These constructions yield new families of asymptotically optimal OOSPCs.

Frequency hopping sequences (FHSs) with favorable partial Hamming correlation properties have important applications in many synchronization and multiple-access systems. In this paper, we investigate constructions of FHSs and FHS sets with optimal partial Hamming correlation. We first establish a correspondence between FHS sets with optimal partial Hamming correlation and multiple partition-type balanced nested cyclic difference packings with a special property. By virtue of this correspondence, some FHSs and FHS sets with optimal partial Hamming correlation are constructed from various combinatorial structures, such as cyclic difference packings and cyclic relative difference families. As a consequence, our constructions yield new FHSs and FHS sets with optimal partial Hamming correlation.

Frequency hopping sequences (FHSs) are employed to mitigate the interferences caused by the hits of frequencies in frequency hopping spread spectrum systems. In this paper, we present combinatorial constructions for FHS sets, including direct constructions by using cyclotomic classes, recursive constructions based on cyclic difference matrices, merging blocks, and discrete logarithm. By these constructions, a number of series of new FHS sets are then produced. These FHS sets are optimal with respect to the Peng-Fan bounds.

We study (symbol-pair) codes for symbol-pair read channels introduced recently by Cassuto and Blaum (2010). A Singleton-type bound on symbol-pair codes is established and infinite families of optimal symbol-pair codes are constructed. These codes are maximum distance separable (MDS) in the sense that they meet the Singleton-type bound. In contrast to classical codes, where all known q-ary MDS codes have length O(q), we show that q-ary MDS symbol-pair codes can have length Ω(q2). In addition, we completely determine the existence of MDS symbol-pair codes for certain parameters.

Multimedia fingerprinting is an effective technique to trace the sources of pirate copies of copyrighted multimedia information. Separable codes can be used to construct fingerprints resistant to the averaging collusion attack on multimedia contents. In this paper, we investigate -separable codes from a combinatorial point of view. We first derive several upper bounds on the sizes of -separable codes, and then turn our attention to the constructions of optimal -separable codes with short length. Two infinite families of optimal -separable codes of length 2 are constructed from projective planes, and all optimal -separable codes of length 3 are explicitly constructed by means of difference matrices. These optimal -separable codes with short length can be used to construct good -separable codes with long length by a known composition construction.

A Steiner quadruple system of order v, denoted by SQS(v), is a pair $(X,{\cal B}),$ where X is a v-set of points and ${\cal B}$ is a set of 4-subsets of X, called blocks, with the property that every 3-subset of X is contained in exactly one block of ${\cal B}$. An SQS(v) is resolvable if its block set can be partitioned into parallel classes. In 1987, Hartman showed that the necessary condition $v\equiv 4$ or $8\ (\rm {mod}\ 12)$ for the existence of a resolvable SQS(v) is sufficient with 23 possible exceptions. In this paper, we construct resolvable SQS(v)s for the 23 undecided orders.