The b-symbol weight hierarchy of the Kasami codes

12/07/2021

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by   Hongwei Zhu, et al.

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The symbol-pair read channel was first proposed by Cassuto and Blaum. Later, Yaakobi et al. generalized it to the b-symbol read channel. It is motivated by the limitations of the reading process in high density data storage systems. One main task in b-symbol coding theory is to determine the b-symbol weight hierarchy of codes. In this paper, we study the b-symbol weight hierarchy of the Kasami codes, which are well known for their applications to construct sequences with optimal correlation magnitudes. The complete symbol-pair weight distribution of the Kasami codes is determined.