Self-orthogonal codes from plateaued functions and their applications in quantum codes and LCD codes

TL;DR

This paper introduces new classes of self-orthogonal linear codes derived from plateaued functions, which are used to construct optimal quantum and LCD codes, expanding the toolkit for quantum error correction and code design.

Contribution

It presents a novel construction of self-orthogonal codes from plateaued functions that do not contain the all-1 vector, and applies these to develop new quantum and LCD codes.

Findings

Explicit weight distributions of the constructed codes

Conditions under which codes are self-orthogonal

New families of optimal quantum and LCD codes

Abstract

Self-orthogonal codes have received great attention due to their important applications in quantum codes, LCD codes and lattices. Recently, several families of self-orthogonal codes containing the all-$1$ vector were constructed by augmentation technique. In this paper, utilizing plateaued functions, we construct some classes of linear codes which do not contain the all-$1$ vector. We also investigate their punctured codes. The weight distributions of the constructed codes are explicitly determined. Under certain conditions, these codes are proved to be self-orthogonal. Furthermore, some classes of optimal linear codes are obtained from their duals. Using the self-orthogonal punctured codes, we also construct several new families of at least almost optimal quantum codes and optimal LCD codes.