The deep hole 问题 of generalized Reed-Solomon codes
摘要
Generalized Reed-Solomon codes are a very important family of error-correcting codes in the theoretical research and practical applications. The study on the structures of generalized Reed-Solomon codes is always a hot topic in coding theory and theoretical computer science. A deep hole of a given error-correcting code is an extremal structure that achieves the maximal error distance. Therefore, to determine deep holes of an error-correcting code is of significant importance in coding theory. In this paper, we review the results on deep holes of generalized Reed-Solomon codes, including the development of the deep hole 问题, research methods, main results, the related finite geometry 问题, and the computing 问题.
引用本文（GB/T 7714）
Zhang Jun, Haiyan Zhou. The deep hole 问题 of generalized Reed-Solomon codes[J]. Scientia Sinica Mathematica, 2023.
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