2025/12/06 by Sudan, Madhu
Computer Science · #Cellular Automata and Applications #Coding theory and cryptography #Computability, Logic, AI Algorithms #Computational Complexity (cs.CC) #E.4 #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2512.06478
openalex publication_date 2025/12/06 · openalex created_date 2025/12/10 · openalex updated_date 2026/07/28
We survey the notion and history of error-correcting codes and the algorithms needed to make them effective in information transmission. We then give some basic as well as more modern constructions of, and algorithms for, error-correcting codes that depend on relatively simple elements of applied algebra. While the role of algebra in the constructions of codes has been widely acknowledged in texts and other writings, the role in the design of algorithms is often less widely understood, and this survey hopes to reduce this difference to some extent.