Infinite families of $2$-designs from two classes of linear codes

TL;DR

This paper constructs infinite families of 2-designs from the supports of codewords in two classes of linear codes by analyzing their weight distributions, enriching the connection between coding theory and combinatorial designs.

Contribution

It explicitly derives infinite families of 2-designs from two classes of linear codes through weight distribution analysis, providing new examples and parameters.

Findings

Infinite families of 2-designs constructed from linear codes

Explicit parameters of the derived 2-designs obtained

Weight distributions of the codes determined

Abstract

The interplay between coding theory and $t$-designs has attracted a lot of attention for both directions. It is well known that the supports of all codewords with a fixed weight in a code may hold a $t$-design. In this paper, by determining the weight distributions of two classes of linear codes, we derive infinite families of $2$-designs from the supports of codewords with a fixed weight in these codes, and explicitly obtain their parameters.