The error coefficient of a linear code, defined as the number of its minimum weight codewords, is a key performance metric to evaluate codes with a given length, dimension, and minimum distance. In this paper, we propose novel approaches, different from existing methods, to produce three new families of binary optimal linear codes with the smallest possible error coefficients. These codes are known as asymptotic frame error rate (AFER)-optimal codes, achieving the best known performance in the additive white Gaussian noise channel and under maximum-likelihood decoding. In particular, we solve a conjecture originally proposed by Li et al. in (IEEE Trans. Inf. Theory 71(7): 5144-5153, 2025).

The error coefficient of a linear code, defined as the number of minimum-weight codewords, plays a central role in evaluating the performance of the code. In this paper, we establish two recursive bounds on the minimum possible error coefficient among optimal linear codes with prescribed parameters. We prove that these bounds are tight in infinitely many cases by constructing two explicit infinite families of optimal linear codes that attain them with equality, and we further show that MDS codes also meet one of the proposed bounds with equality. Beyond the recursive-bound framework, we determine the minimum possible error coefficient for three explicit families of optimal linear codes: two families arising from simplex codes and one family associated with MacDonald codes. Moreover, employing tools from combinatorial design theory, we solve a problem proposed by Guanet al.[12] on the eventual constancy of the minimum error coefficient of optimal codes.

Annotating remote sensing object recognition needs high professionalism, and thus limited labeled samples are available. Suffering from this, general remote sensing object recognition methods are facing low recognition accuracy. Addressing this issue, this paper proposes a diversity consistency learning for remote sensing object recognition with limited labels. Specifically, diversity generation model is designed as a teacher model to generate diverse results, which is trained with labeled samples. Then, round consistency distillation model is introduced to distill the knowledge of diverse pseudo labels to a student network, which is trained with unlabeled samples. Especially, diverse pseudo labels are generated by the well-trained diversity generation model, which can improve recognition accuracy since diverse pseudo label errors can cancel each other out. Extensive experiments on two widely-used datasets of FS23 and HRSC2016 demonstrate the superior performance of our method compared with the state of the arts.

Fine-grained object classification (FGOC) focuses on identifying subcategories of objects, which is crucial in military and civilian. Existing FGOC methods primarily focus on high-resolution aerial images, limiting their application on low-resolution (LR) FGOC that is a more realistic setting, especially on resource-constrained satellite devices. It is more challenging to deal with LR FGOC since objects’ details are blurred or missing. Addressing this issue, we make the first attempt to explore LR FGOC and propose a novel pipeline based on two technical insights: 1) feature balance strategy discriminatively integrates super-resolution weak and strong detailed presentations into coarse features of LR aerial images, achieving a feature balance to avoid that the weak detailed presentations are inhibited by the strong ones and 2) iterative interaction mechanism alternately refines feature details of the discriminative ship regions and optimizes the performance of FGOC. Moreover, we build a low-resolution fine-grained object (LFS) dataset to promote further study and evaluation. Extensive experiments on the proposed LFS dataset and the other three object datasets of DOTA, FS23, and HRSC2016 demonstrate that our method outperforms state-of-the-art algorithms. Dataset and code are publicly available athttps://github.com/wdzhao123/FBNet.