The connections among Hamming metric, b-symbol metric, and r-th generalized Hamming metric

09/28/2021

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by   Minjia Shi, et al.

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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. we explore the combinatorial function of the size of the b-symbol weight set of a code C.