The Connections Among Hamming Metric, b-Symbol Metric, and r-th Generalized Hamming Metric
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Date
2023Metadata
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Original version
IEEE Transactions on Information Theory. 2023, 69 (4), 2485 - 2493. 10.1109/TIT.2023.3239543Abstract
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.