Dictionary Based Pattern Entropy for Causal Direction Discovery

This paper introduces Dictionary Based Pattern Entropy (DPE), a novel framework that combines Algorithmic and Shannon Information Theories to infer causal directions and identify driving subpatterns in symbolic sequences by quantifying how compact, rule-based patterns in a cause systematically reduce uncertainty in an effect, demonstrating robust performance across diverse synthetic and real-world datasets.

Harikrishnan N B, Shubham Bhilare, Aditi Kathpalia + 1 more2026-03-06🔢 math

Improved Decoding of Quantum Tanner Codes Using Generalized Check Nodes

This paper proposes an enhanced iterative belief propagation decoder for quantum Tanner codes that groups check nodes into generalized checks decoded via maximum a posteriori methods, demonstrating significant performance gains over existing decoders in finite-length settings while identifying limited benefits for other qLDPC code families through both empirical results and theoretical cycle analysis.

Olai \AA. Mostad, Eirik Rosnes, Hsuan-Yin Lin2026-03-06⚛️ quant-ph

Differential Goppa Codes

This paper provides a rigorous generalization of Rosenbloom and Tsfasman's algebraic-geometric codes to arbitrary genus curves by defining differential Goppa codes via nn-jets and Hasse-Schmidt derivatives, analyzing their structural properties and distance variations, and establishing that they encompass all linear codes on P1\mathbb{P}^1 while strictly generalizing classical Goppa codes.

David González González, Ángel Luis Muñoz Castañeda, Luis Manuel Navas Vicente2026-03-05🔢 math

When Relaxation Does Not Help: RLDCs with Small Soundness Yield LDCs

This paper demonstrates that any non-adaptive qq-query relaxed locally decodable code (RLDC) with sufficiently small soundness error can be converted into a standard qq-query locally decodable code (LDC) with comparable parameters, thereby generalizing previous separation results and yielding improved lower bounds for RLDCs, relaxed locally correctable codes (RLCCs), and probabilistically checkable proofs of proximity (PCPPs).

Kuan Cheng, Xin Li, Songtao Mao2026-03-05🔢 math