Optimal Ferrers Diagram Rank-Metric Codes: New Constructions, Diagram Combinations, and Applications to Constant-Dimension Subspace Codes
本文通过从最大秩距离码的子码中构造,提出了三种新的最优Ferrers图秩度量码构建方法,解决了特定参数下FDRM码的最优性问题。
本文通过从最大秩距离码的子码中构造,提出了三种新的最优Ferrers图秩度量码构建方法,解决了特定参数下FDRM码的最优性问题。
为解决自动驾驶中全视角覆盖与计算效率的问题,SV-WAM通过共享生成模型进行动作学习,并采用可行驶区域合规正则化器提高安全性。
研究提出FlightLLM,一种基于先验引导的语义大语言模型方法,通过特征工程、语义离散化及少量样本对比学习等手段解决飞行安全事件解释问题。
This work addresses the challenges of cross-view geolocalization, including large viewpoint discrepancies, inconsistent textures, and degraded local discriminative cues. To this end, the authors propose the Spatial and Frequency Domain Enhancement network (SFDE), which introduces frequency-domain invariance into this task for the first time. SFDE employs a parallel three-branch architecture to jointly model global semantics, local geometric structures, and frequency-domain statistical properties, enabling multi-granularity consistent representations. By integrating multi-scale geometric modeling with progressive enhancement and coupled constraint optimization within a unified embedding space, the method achieves state-of-the-art or competitive performance across multiple benchmarks, significantly improving retrieval and localization accuracy while maintaining a lightweight and efficient design.
This paper addresses the low lower bound on minimum distance in constant-dimension codes (CDCs). To tackle this, we propose a multi-level construction method based on one-factorizations of complete graphs. Our key innovation lies in designing novel skeleton codes via binary vector transformations induced by one-factorizations, and integrating quasi-pendant block structures with optimal Ferrers diagram rank-metric codes to construct CDCs achieving high minimum distance. The approach systematically refines the multi-level construction framework: while fixing the dimension $k = 6$ and minimum distance $d = 8$, it significantly improves the cardinality lower bounds for code lengths $n in [16,19]$, thereby advancing the state-of-the-art lower bounds on $overline{A}_q(n,8,6)$. This work provides both new theoretical insights and practical construction tools for network coding and random linear network coding over finite fields.
本文通过从最大秩距离码的子码中构造,提出了三种新的最优Ferrers图秩度量码构建方法,解决了特定参数下FDRM码的最优性问题。
为解决自动驾驶中全视角覆盖与计算效率的问题,SV-WAM通过共享生成模型进行动作学习,并采用可行驶区域合规正则化器提高安全性。
研究提出FlightLLM,一种基于先验引导的语义大语言模型方法,通过特征工程、语义离散化及少量样本对比学习等手段解决飞行安全事件解释问题。
This work addresses the challenges of cross-view geolocalization, including large viewpoint discrepancies, inconsistent textures, and degraded local discriminative cues. To this end, the authors propose the Spatial and Frequency Domain Enhancement network (SFDE), which introduces frequency-domain invariance into this task for the first time. SFDE employs a parallel three-branch architecture to jointly model global semantics, local geometric structures, and frequency-domain statistical properties, enabling multi-granularity consistent representations. By integrating multi-scale geometric modeling with progressive enhancement and coupled constraint optimization within a unified embedding space, the method achieves state-of-the-art or competitive performance across multiple benchmarks, significantly improving retrieval and localization accuracy while maintaining a lightweight and efficient design.
This paper addresses the low lower bound on minimum distance in constant-dimension codes (CDCs). To tackle this, we propose a multi-level construction method based on one-factorizations of complete graphs. Our key innovation lies in designing novel skeleton codes via binary vector transformations induced by one-factorizations, and integrating quasi-pendant block structures with optimal Ferrers diagram rank-metric codes to construct CDCs achieving high minimum distance. The approach systematically refines the multi-level construction framework: while fixing the dimension $k = 6$ and minimum distance $d = 8$, it significantly improves the cardinality lower bounds for code lengths $n in [16,19]$, thereby advancing the state-of-the-art lower bounds on $overline{A}_q(n,8,6)$. This work provides both new theoretical insights and practical construction tools for network coding and random linear network coding over finite fields.