Three Weight Ternary Linear Codes from Non-Weakly Regular Bent Functions

TL;DR

This paper introduces a novel method for constructing three-weight ternary linear codes using non-weakly regular dual-bent functions and their associated subspaces, enabling flexible code parameters and detailed weight distribution analysis.

Contribution

It presents a new construction approach for three-weight ternary linear codes based on non-weakly regular dual-bent functions and their pre-image sets, expanding code parameter options.

Findings

Constructed several classes of three-weight ternary codes

Provided explicit weight distributions for the codes

Offered multiple examples demonstrating the method's effectiveness

Abstract

In this paper, several classes of three-weight ternary linear codes from non-weakly regular dual-bent functions are constructed based on a generic construction method. Instead of the whole space, we use the subspaces $B_+(f)$ or $B_-(f)$ associated with a ternary non-weakly regular dual-bent function $f$. Unusually, we use the pre-image sets of the dual function $f^*$ in $B_+(f)$ or $B_-(f)$ as the defining sets of the corresponding codes. Since the size of the defining sets of the constructed codes is flexible, it enables us to construct several codes with different parameters for a fixed dimension. We represent the weight distribution of the constructed codes. We also give several examples.