Generalized Hamming weights of three classes of linear codes

TL;DR

This paper studies the generalized Hamming weights of three classes of linear codes, providing new results and solving an open problem in the semiprimitive case, which enhances understanding of their cryptographic properties.

Contribution

It determines the generalized Hamming weights for three classes of linear codes and resolves an open problem in the semiprimitive case from previous research.

Findings

Partially determined generalized Hamming weights for the codes

Solved an open problem in the semiprimitive case

Enhanced understanding of code cryptography performance

Abstract

The generalized Hamming weights of a linear code have been extensively studied since Wei first use them to characterize the cryptography performance of a linear code over the wire-tap channel of type II. In this paper, we investigate the generalized Hamming weights of three classes of linear codes constructed through defining sets and determine them partly for some cases. Particularly, in the semiprimitive case we solve an problem left in Yang et al. (IEEE Trans. Inf. Theory 61(9): 4905--4913, 2015).