The construction and weight distributions of all projective binary linear codes

TL;DR

This paper explores the relationship between the weight distributions of all projective binary linear codes and the Walsh spectra of Boolean functions, highlighting new research directions in coding theory.

Contribution

It establishes a connection between code weight distributions and Boolean function spectra, proposing new research problems in the field.

Findings

Identifies a link between projective binary linear codes and Boolean function spectra

Proposes new research problems related to code weight distributions and Walsh spectra

Highlights potential for further exploration in coding theory and Boolean functions

Abstract

Boolean functions can be used to construct binary linear codes in many ways, and vice versa. The objective of this short article is to point out a connection between the weight distributions of all projective binary linear codes and the Walsh spectra of all Boolean functions. New research problems are also proposed.