# The Weight Hierarchy of a Family of Cyclic Codes with Arbitrary Number of Nonzeroes

## TL;DR

This paper investigates the generalized Hamming weights of a specific family of cyclic codes with any number of nonzeroes, using number theory to determine their weight hierarchy.

## Contribution

It extends previous work by analyzing the GHWs of cyclic codes with arbitrary nonzeroes through a novel number-theoretic approach.

## Key findings

- Determined the weight hierarchy for the studied cyclic codes.
- Provided explicit formulas for GHWs based on code parameters.
- Enhanced understanding of the structure of cyclic codes with multiple nonzeroes.

## Abstract

The generalized Hamming weights (GHWs) are fundamental parameters of linear codes. GHWs are of great interest in many applications since they convey detailed information of linear codes. In this paper, we continue the work of [10] to study the GHWs of a family of cyclic codes with arbitrary number of nonzeroes. The weight hierarchy is determined by employing a number-theoretic approach.