Advances in Coding Theory and Practice

The field of coding theory is witnessing significant developments, with a focus on innovative methods for constructing efficient codes, advancing the understanding of code-based cryptography, and improving the reliability of coded computing systems. Researchers are exploring new approaches to coded caching, distributed computing, and molecular communication, with a emphasis on mitigating intersymbol interference and improving code rates. Notably, the application of quasi-twisted codes, linear complementary pairs, and vectorial dual-bent functions are leading to breakthroughs in code construction and cryptosystems. Furthermore, the development of secure coded computing frameworks, such as Secure Berrut Approximated Coded Computing, is enhancing the robustness of distributed computing systems against erroneous computations. The study of feedback schemes for dirty paper channels with state estimation at the receiver is also yielding capacity-achieving schemes, highlighting the importance of feedback in constructing low-complexity coding schemes. Some particularly noteworthy papers in this regard include: the construction of linear complementary pairs of algebraic geometry codes via Kummer extensions, which is enabling the construction of explicit LCPs of MDS AG Codes from elliptic function fields. Additionally, the proposal of a syndrome-based decoding method for quasi-twisted codes is providing an efficient means of correcting errors in these codes.

Sources

Linear Complementary Pairs of Algebraic Geometry Codes via Kummer Extensions

Hybrid Character Sums From Vectorial Dual-Bent Functions and Asymptotically Optimal Complex Codebooks With Small Alphabet Sizes

Elias' Encoding from Lagrangians and Renormalization

ISI-Aware Code Design: A Linear Approach Towards Reliable Molecular Communication

Combinatorial Multi-Access Coded Caching with Private Caches under Intersecting Index Constraints

On the Optimality of Coded Distributed Computing for Ring Networks

On the rank weight hierarchy of $M$-codes

On Hierarchical Coded Caching with Offline Users

Optimal Feedback Schemes for Dirty Paper Channels With State Estimation at the Receiver

Quasi-twisted codes: decoding and applications in code-based cryptography

On Securing Berrut Approximated Coded Computing Through Discrete Cosine Transforms

Coding for Quasi-Static Fading Channel with Imperfect CSI at the Transmitter and Quantized Feedback

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