Intersection sets, three-character multisets and associated codes

TL;DR

This paper constructs new minimal intersection sets in affine spaces and develops associated linear error-correcting codes with few weights, also introducing three-character multisets in projective spaces and analyzing their weight distributions.

Contribution

It introduces novel minimal intersection sets with three intersection numbers and new three-character multisets, along with their weight distributions.

Findings

Constructed minimal intersection sets with three intersection numbers.

Developed linear codes with few weights from these sets.

Determined weight enumerators and distributions for the codes and multisets.

Abstract

In this article we construct new minimal intersection sets in ${\mathrm{AG}}(r,q^2)$ sporting three intersection numbers with hyperplanes; we then use these sets to obtain linear error correcting codes with few weights, whose weight enumerator we also determine. Furthermore, we provide a new family of three-character multisets in ${\mathrm{PG}}(r,q^2)$ with $r$ even and we also compute their weight distribution.