Complete b-symbol weight distribution of some irreducible cyclic codes

TL;DR

This paper derives the complete b-symbol weight distribution for a class of irreducible cyclic codes, advancing understanding of their error-correcting capabilities in b-symbol read channels.

Contribution

It provides the first complete b-symbol weight distribution for irreducible cyclic codes with two nonzero weights, expanding the theoretical framework.

Findings

Derived the complete b-symbol weight distribution for specific irreducible codes.

Identified codes with exactly two nonzero b-symbol weights.

Enhanced understanding of code performance in b-symbol error correction.

Abstract

Recently, $b$-symbol codes are proposed to protect against $b$-symbol errors in $b$-symbol read channels. It is an interesting subject of study to consider the complete $b$-symbol weight distribution of cyclic codes since $b$-symbol metric is a generalization for Hamming metric. The complete $b$-symbol Hamming weight distribution of irreducible codes is known in only a few cases. In this paper, we give a complete $b$-symbol Hamming weight distribution of a class of irreducible codes with two nonzero $b$-symbol Hamming weights.