论文标题
最佳二进制LCD代码
Optimal Binary LCD Codes
论文作者
论文摘要
线性互补的双码代码（或具有互补双重的代码）是代码，其与双重代码相交的代码是微不足道的。这些代码首先是由Massey于1964年引入的。如今，LCD代码在文献中进行了广泛的研究，并广泛应用于数据存储，密码学等。在本文中，我们证明了使用它们的简短和刺破的代码证明了二进制LCD代码的某些属性。我们还以最大的最小重量$ d_ {lcd}（n，k）$呈现一些不等式的二进制lcd [n，k]代码，用于给定的长度n和尺寸k。此外，我们给出了两个表，其中$ d_ {lcd}（lcd}（n，k）$的值$ k \ le 32 $和$ n \ le 40 $，以及两个带有分类结果的表。
Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. These codes were first introduced by Massey in 1964. Nowadays, LCD codes are extensively studied in the literature and widely applied in data storage, cryptography, etc. In this paper, we prove some properties of binary LCD codes using their shortened and punctured codes. We also present some inequalities for the largest minimum weight $d_{LCD}(n,k)$ of binary LCD [n,k] codes for given length n and dimension k. Furthermore, we give two tables with the values of $d_{LCD}(n,k)$ for $k\le 32$ and $n\le 40$, and two tables with classification results.
