No abstract

A new construction of the self-dual, doubly-even and extremal [48, 24, 12] binary linear block code is given. The construction is much like that of a cyclic code from a polynomial. A zero divisor in a group ring with an underlying dihedral group generates the code. A proof that the code is of minimum distance twelve, without need to resort to computation by computer, is outlined. We also prove the code is self-dual, doubly even and that the code is an ideal in the group ring. The underlying group ring structure is used, which offers a number of useful generator matrices for the code. Interestingly, the construction involves unipotent elements within the group ring, and these lead to the creation of weighing matrices.

No abstract

In this paper, we present a robust prototype learning framework for anomalous sound detection (ASD), where prototypical loss is exploited to measure the similarity between samples and prototypes. We show that existing generative and discriminative based ASD methods can be unified into this framework from the perspective of prototypical learning. For ASD in recent DCASE challenges, extensions related to imbalanced learning are proposed to improve the robustness of prototypes learned from source and target domains. Specifically, balanced sampling and multiple-prototype expansion (MPE) strategies are proposed to address imbalances across attributes of source and target domains. Furthermore, a novel negative-prototype expansion (NPE) method is used to construct pseudo-anomalies to learn a more compact and effective embedding space for normal sounds. Evaluation on the DCASE2022 Task2 development dataset demonstrates the validity of the proposed prototype learning framework.

No abstract