论文标题
$ \ f_4 $上的添加互补双代码
Additive complementary dual codes over $\F_4$
论文作者
论文摘要
线性代码是线性互补双重（LCD），如果它毫无用处地符合其双重。由于登陆电子设备的安全性，LCD代码最近一直是一个热门话题（Carlet and Guilley，2014年）。 $ \ f_4 $上方的添加代码是$ \ f_4 $ - 代码，它们是通过CodeWord添加而稳定的，但不一定是标量乘法。如果$ \ f_4 $上的添加代码是添加剂互补的双重（ACD），则它是微不足道的。这项研究的目的是研究这些代码，这些代码符合其双重符合其双重的代码。用于研究LCD代码的所有技术和问题可能与ACD代码有关。从二元代码的ACD代码的有趣构造相对于痕量赫尔米尼亚和跟踪欧几里得内部产物。前产品与量子代码有关。
A linear code is linear complementary dual (LCD) if it meets its dual trivially. LCD codes have been a hot topic recently due to Boolean masking application in the security of embarked electronics (Carlet and Guilley, 2014). Additive codes over $\F_4$ are $\F_4$-codes that are stable by codeword addition but not necessarily by scalar multiplication. An additive code over $\F_4$ is additive complementary dual (ACD) if it meets its dual trivially. The aim of this research is to study such codes which meet their dual trivially. All the techniques and problems used to study LCD codes are potentially relevant to ACD codes. Interesting constructions of ACD codes from binary codes are given with respect to the trace Hermitian and trace Euclidean inner product. The former product is relevant to quantum codes.
