Construction of binary LCD codes, ternary LCD codes and quaternary Hermitian LCD codes

TL;DR

This paper introduces two novel methods to construct binary LCD, ternary LCD, and quaternary Hermitian LCD codes, improving the lower bounds on their largest minimum weights through modifications of existing self-dual code construction techniques.

Contribution

The paper presents new construction methods for LCD codes that enhance known bounds on minimum weights, expanding the types of LCD codes available.

Findings

Constructed binary LCD codes with improved minimum weights

Developed quaternary Hermitian LCD codes with better bounds

Provided systematic methods for generating LCD codes from existing codes

Abstract

We give two methods for constructing many linear complementary dual (LCD for short) codes from a given LCD code, by modifying some known methods for constructing self-dual codes. Using the methods, we construct binary LCD codes and quaternary Hermitian LCD codes, which improve the previously known lower bound on the largest minimum weights.