The Connections Among Hamming Metric, b -Symbol Metric, and r -th Generalized Hamming Metric
Minjia Shi, Hongwei Zhu, Tor Helleseth · IEEE Transactions on Information Theory · 2023
The$r$-th generalized Hamming metric and the$b$-symbol metric are two different generalizations of Hamming metric. The former is used on the wire-tap channel of Type II, and the latter is motivated by the limitations of the reading process in high-density data storage systems and applied to a read channel that outputs overlapping symbols. In this paper, we study the connections among the three metrics (that is, Hamming metric,$b$-symbol metric, and$r$-th generalized Hamming metric) mentioned above and give a conjecture about the$b$-symbol Griesmer Bound for cyclic codes.