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cs.IT2026
Evolving Towards Better Codes: LLM-Guided Search for High-Distance Binary Linear Codes
Amal Seddas, Vladyslav Shashkov, Maryna Viazovska +1
Evolutionary program search driven by large language models (LLMs) has produced record-breaking constructions for open problems in combinatorics and beyond. We apply this approach…
cs.IT2024
Polynomial Freiman-Ruzsa, Reed-Muller codes and Shannon capacity
Emmanuel Abbe, Colin Sandon, Vladyslav Shashkov +1
In 1948, Shannon used a probabilistic argument to show the existence of codes achieving a maximal rate defined by the channel capacity. In 1954, Muller and Reed introduced a simple…