Griesmer bound and constructions of linear codes in b-symbol metric

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Official URL: https://dx.doi.org/10.1109/TIT.2024.3423702

The b -symbol metric is a generalization of the Hamming metric. Linear codes in the b -symbol metric have been used in the read channel whose outputs consist of b consecutive symbols. The Griesmer bound outperforms the Singleton bound for F q -linear codes in the Hamming metric, when q is fixed and the length is large enough. This scenario is also applicable in the b -symbol metric. Shi, Zhu, and Helleseth recently made a conjecture on cyclic codes in the b -symbol metric. In this paper, we present the b -symbol Griesmer bound for linear codes by concatenating linear codes and simplex codes. Based on cyclic codes and extended cyclic codes, we propose two families of distance-optimal linear codes with respect to the b -symbol Griesmer bound.