The Connections Among Hamming Metric, <i>b</i>-Symbol Metric, and <i>r</i>-th Generalized Hamming Metric

The $r$ -th generalized Hamming metric and the notation="LaTeX">$b$ -symbol are two different generalizations of metric. former is used on wire-tap channel Type II, latter motivated by limitations reading process in high-density data storage systems applied to a read that outputs overlapping symbols. In this paper, we study connections among three metrics (that is, metric, metric) mentioned above give conjecture about Griesmer Bound for cyclic codes.