Symplectic self-orthogonal and LCD codes from the Plotkin sum construction

TL;DR

This paper introduces new criteria and constructions for symplectic self-orthogonal and LCD codes using the Plotkin sum, resulting in codes with improved parameters and asymptotic goodness.

Contribution

It provides novel criteria and explicit constructions for symplectic SO and LCD codes, including classes with optimal parameters and asymptotic properties.

Findings

Derived symplectic MDS codes with good parameters

Constructed binary symplectic LCD codes outperforming known codes

Proved asymptotic goodness of the constructed codes

Abstract

In this work, we propose two criteria for linear codes obtained from the Plotkin sum construction being symplectic self-orthogonal (SO) and linear complementary dual (LCD). As specific constructions, several classes of symplectic SO codes with good parameters including symplectic maximum distance separable codes are derived via $\ell$-intersection pairs of linear codes and generalized Reed-Muller codes. Also symplectic LCD codes are constructed from general linear codes. Furthermore, we obtain some binary symplectic LCD codes, which are equivalent to quaternary trace Hermitian additive complementary dual codes that outperform best-known quaternary Hermitian LCD codes reported in the literature. In addition, we prove that symplectic SO and LCD codes obtained in these ways are asymptotically good.