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arXiv · 2208.07708

Construction Methods for Galois LCD codes over Finite Fields

Gyanendra K. Verma·Astha Agrawal·R. K. Sharma
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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 $26\leq n \leq 40$, and $21 \leq k \leq 30$. Also, optimal 2-Galois LCD codes over $\mathbb{F}_{2^3}$ for code length, $1 \leq n \leq 15$ have been obtained. Finally, we extend some previously known results to the $\sigma$-inner product from Euclidean inner product.

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Gyanendra K. Verma, Astha Agrawal, R. K. Sharma. 2022-08-16. Construction Methods for Galois LCD codes over Finite Fields. https://arxiv.org/abs/2208.07708

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