Linear codes for b-symbol read channels attaining the Griesmer bound

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Kurz, Sascha:
Linear codes for b-symbol read channels attaining the Griesmer bound.
Bayreuth , 2025 . - 27 S.

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Abstract

Reading channels where $b$-tuples of adjacent symbols are read at every step have e.g. applications in storage. Corresponding bounds and constructions of codes for the b-symbol metric, especially the pair-symbol metric where b=2, were intensively studied in the last fifteen years. Here we determine the optimal code parameters of linear codes in the b-symbol metric assuming that the minimum distance is sufficiently large. We also determine the optimal parameters of linear binary codes in the pair-symbol metric for small dimensions.