Three Families of Projective Binary Linear Codes of at Most Four Weights

TL;DR

This paper constructs three classes of binary linear codes with at most four weights, including two projective three-weight codes, and applies them to create s-sum sets for odd s > 1.

Contribution

It introduces three new families of binary linear codes with limited weights, expanding the known code constructions and their applications.

Findings

Constructed three classes of binary linear codes with at most four weights.

Two of the classes are projective three-weight codes.

Applied the codes to construct s-sum sets for any odd s > 1.

Abstract

Three classes of binary linear codes with at most four nonzero weights were constructed in this paper, in which two of them are projective three-weight codes. As applications, $s$-sum sets for any odd $ s > 1$ were constructed.