Self-orthogonal codes from plateaued functions

TL;DR

This paper introduces a novel family of self-orthogonal linear codes derived from plateaued functions, with applications in quantum computing and lattice theory, demonstrating optimal or near-optimal extendability and new LCD code parameters.

Contribution

It constructs new self-orthogonal codes from plateaued functions and derives related LCD and self-dual codes, expanding coding theory applications.

Findings

Constructed linear codes with four nonzero weights from plateaued functions

Proved codes are self-orthogonal and nearly optimally extendable

Derived new parameters for binary and ternary LCD codes

Abstract

Self-orthogonal codes are of interest as they have important applications in quantum codes, lattices and many areas. In this paper, based on the weakly regular plateaued functions or plateaued Boolean functions, we construct a family of linear codes with four nonzero weights. This family of linear codes is proved to be not only self-orthogonal but also optimally or almost optimally extendable. Besides, we derive binary and ternary linearly complementary dual codes (LCD codes for short) with new parameters from this family of codes. Some families of self-dual codes are also obtained as byproducts.