Construction Methods for Galois LCD codes over Finite Fields

Abstract

In this article, first we present a method for constructing many Hermitian LCD codes from a given Hermitian LCD code, and then provide several methods which utilize either a given [n, k, d] linear code or a given [n, k, d] Galois LCD code to construct new Galois LCD codes with different parameters. Using these construction methods, we construct several new [n, k, d] ternary LCD codes with better parameters for $26\le n\le 40$, and $21\le k\le 30$. Also, optimal 2-Galois LCD codes over ${\mathbb{F}}_{2^3}$ for code length, $1\le n\le 15$ have been obtained. Finally, we extend some previously known results to the $\sigma$-inner product from Euclidean inner product.

There are several mathematical and English language typos we will submit a new one soon