The b-symbol weight hierarchy of the Kasami codes

TL;DR

This paper investigates the $b$-symbol weight hierarchy of Kasami codes, providing a complete weight distribution, which is crucial for applications in high-density data storage systems.

Contribution

It determines the complete $b$-symbol weight distribution of Kasami codes, advancing understanding of their structure in $b$-symbol coding theory.

Findings

Complete $b$-symbol weight distribution of Kasami codes determined

Enhanced understanding of Kasami codes for high-density storage

Contributes to $b$-symbol coding theory development

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.