Department of Mathematics - Seminar on Pure Mathematics - Deep Holes of RS-codes and non RS-codes

A deep hole is the extremal structure that reaches the maximum error distance of an error-correcting code. Determining the deep holes of error-correcting codes is of great significance in coding theory. Reed-Solomon codes (RS-codes) are a very important class of error-correcting codes in both theoretical research and practical applications. The study of their structure has always been a hot topic in coding theory and theoretical computer science. The study of the construction and related properties of non-Reed-Solomon codes is also a hot topic in recent years. This report reviews the research progress on deep holes of RS-codes and non RS-codes, including the development of the problem, research methods, main conclusions, and related finite geometry and computational issues.