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arXiv · 2112.04019

The b-symbol weight hierarchy of the Kasami codes

Hongwei Zhu·Minjia Shi
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Abstract

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.

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Hongwei Zhu, Minjia Shi. 2021-12-07. The b-symbol weight hierarchy of the Kasami codes. https://arxiv.org/abs/2112.04019

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