Letqbe an odd prime power with$q\equiv 3\ ({\mathrm {mod}}\,4)$. In this paper, we study the differential and boomerang properties of the function$F_{2,u}(x)=x^{2}\big (1+u\eta (x)\big)$over$\mathbb {F}_{q}$, where$u\in \mathbb {F}_{q}^{*}$and$\eta $is the quadratic character of$\mathbb {F}_{q}$. We determine the differential uniformity of$F_{2,u}$for any$u\in \mathbb {F}_{q}^{*}$, as well as the differential spectra and boomerang uniformity of the locally-APN functions$F_{2,\pm 1}$, thereby disproving a conjecture proposed in Budaghyan and Pal (2024), which states that there exist infinitely many values ofqandusuch that$F_{2,u}$is an APN function.

In this paper, we employ general results on the value distributions of perfect nonlinear functions from$\mathbb {F}_{p^{m}}$to$\mathbb {F}_{p}$to give a unified approach to determining the weight distributions of two classes of linear codes over$\mathbb {F}_{p}$constructed from perfect nonlinear functions, where$p$is an odd prime and$m$is an odd number. When$m$is even, we give some mild additional conditions for similar conclusions to hold.

Accurate localization is a crucial step for intelligent vehicles (IVs). And vision-based localization methods are promising due to its good accuracy and low cost. However, vision-based methods are usually not robust enough due to the errors of matching similar road scenarios. In this paper, we proposed a visual map-based localization method, called multi-view site matching (MVSM). We proposed using two camera views (i.e., downward-view and front-view) to construct visual map. The visual map consists of a serial of nodes. Each node encodes the features of the road, the 2D structure, and the poses of the vehicle. Based on the constructed visual map, we proposed a multi-scale method for accurate vehicle localization. In coarse localization, we adopt a topological model to obtain a set of candidate nodes from visual map. Furthermore, holistic features from front view are matched within the candidates such that the best matched node is determined for image-level localization. In metric localization, the best matched is first verified with the local features from downward view. And the vehicle pose is finally computed by utilizing the 2D structure from the verified nodes in the map. In the experiment, the proposed MVSM method has been tested with actual field data covering different pavement types in different seasons. The proposed MVSM method can achieve less than 0.20m mean localization errors. Compared to existing vision-based methods, the proposed method utilizes two views to enhance image-level localization and 2D pavement structure to improve metric localization so as to greatly improve the overall localization performance.