Advances in Coding Theory and Algebraic Complexity

The field of coding theory and algebraic complexity is witnessing significant developments, with a focus on improving the efficiency and robustness of coding schemes. Researchers are exploring new approaches to construct optimal codes, such as the use of algebraic geometry codes and trace codes, which have been shown to outperform traditional codes in certain scenarios. Additionally, there is a growing interest in the development of new decoding algorithms, including deterministic list decoding and policy-guided Monte Carlo Tree Search decoders, which offer improved performance and efficiency. Furthermore, the application of machine learning techniques, such as autoencoder-based codes, is being investigated for the design of optimal codes. Noteworthy papers in this area include the proposal of a bivariate Cayley-Hamilton theorem, which has far-reaching implications for algebraic complexity, and the development of generic constructions for optimal-access binary MDS array codes with smaller sub-packetization. Overall, these advances have the potential to significantly impact the field of coding theory and its applications in communication and data storage.

Sources

On the gradient of the coefficient of the characteristic polynomial

Modular composition & polynomial GCD in the border of small, shallow circuits

Adjoint and duality for rank-metric codes in a skew polynomial framework

Deterministic list decoding of Reed-Solomon codes

Shortest self-orthogonal embeddings of binary linear codes

Group Probability Decoding of Turbo Product Codes over Higher-Order Fields

Variable-Length Joint Source-Channel Coding for Semantic Communication

Robust Dynamic Coded Distributed Storage with Partially Storage Constrained Servers

Cartesian square-free codes

Tracing AG Codes: Toward Meeting the Gilbert-Varshamov Bound

Policy-Guided MCTS for near Maximum-Likelihood Decoding of Short Codes

Color Multiset Codes based on Sunmao Construction

Learning Binary Autoencoder-Based Codes with Progressive Training

Generic Construction of Optimal-Access Binary MDS Array Codes with Smaller Sub-packetization

Computability of the Optimizer for Rate Distortion Functions

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