论文标题
有限字段的Galois LCD代码的施工方法
Construction Methods for Galois LCD codes over Finite Fields
论文作者
论文摘要
在本文中，首先，我们提出了一种从给定的Hermitian LCD代码构建许多Hermitian LCD代码的方法，然后提供了几种使用给定的[N，K，D]线性代码或给定的[N，K，D] Galois LCD代码来构建具有不同参数的新Galois LCD代码的方法。使用这些构造方法，我们构建了几个新的[n，k，d]三元LCD代码，具有更好的参数，价格为$ 26 \ leq n \ leq 40 $，$ 21 \ leq k \ leq k \ leq 30 $。此外，对于代码长度，$ \ mathbb {f} _ {2^3} $上的最佳2-GALOIS LCD代码已获得$ 1 \ leq n \ leq 15 $。最后，我们将一些先前已知的结果扩展到欧几里得内部产品的$σ$ -Inner产品。
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 $σ$-inner product from Euclidean inner product.
