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Research Paper#Coding Theory, Error Correction, Decoding Algorithms🔬 ResearchAnalyzed: Jan 3, 2026 16:45

Efficient Decoding Algorithms for Non-GRS Codes

Published:Dec 30, 2025 13:27
1 min read
ArXiv

Analysis

This paper addresses the important problem of decoding non-Generalized Reed-Solomon (GRS) codes, specifically Twisted GRS (TGRS) and Roth-Lempel codes. These codes are of interest because they offer alternatives to GRS codes, which have limitations in certain applications like cryptography. The paper's contribution lies in developing efficient decoding algorithms (list and unique decoding) for these codes, achieving near-linear running time, which is a significant improvement over previous quadratic-time algorithms. The paper also extends prior work by handling more complex TGRS codes and provides the first efficient decoder for Roth-Lempel codes. Furthermore, the incorporation of Algebraic Manipulation Detection (AMD) codes enhances the practical utility of the list decoding framework.
Reference

“The paper proposes list and unique decoding algorithms for TGRS codes and Roth-Lempel codes based on the Guruswami-Sudan algorithm, achieving near-linear running time.”

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Research Paper#Neural Networks, Linear Algebra, Optimization🔬 ResearchAnalyzed: Jan 3, 2026 15:58

SPM: Efficient Linear Transformations for Neural Networks

Published:Dec 30, 2025 00:03
1 min read
ArXiv

Analysis

This paper introduces Stagewise Pairwise Mixers (SPM) as a more efficient and structured alternative to dense linear layers in neural networks. By replacing dense matrices with a composition of sparse pairwise-mixing stages, SPM reduces computational and parametric costs while potentially improving generalization. The paper's significance lies in its potential to accelerate training and improve performance, especially on structured learning problems, by offering a drop-in replacement for a fundamental component of many neural network architectures.
Reference

“SPM layers implement a global linear transformation in $O(nL)$ time with $O(nL)$ parameters, where $L$ is typically constant or $log_2n$.”

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