论文标题
MDS扭曲的芦苇 - 固体代码和LCD MDS代码的新结构
New Constructions of MDS Twisted Reed-Solomon Codes and LCD MDS Codes
论文作者
论文摘要
最大距离可分离（MDS）代码是最佳的，对于给定的长度和代码尺寸，无法提高最小距离。 2017年引入了有限场上的扭曲的芦苇 - 固体代码，这是芦苇 - 固体代码的概括。可以在密码学中应用扭曲的芦苇 - 固体代码，该密码更喜欢最小距离的代码。 MDS代码可以通过扭曲的芦苇固体代码构建，其中大多数不等于芦苇固体代码。在本文中，我们首先将扭曲的芦苇固体代码推广到广义的扭曲的芦苇 - 固体代码，然后给出一些新的MDS（广义）扭曲的Reed芦苇 - 固体代码的新的显式结构。在某些情况下，我们的构造可以获得长度长于以前的作品的构造的MDS代码。线性互补双重（LCD）代码是线性代码，与它们的双重码相交。 LCD代码可以应用于密码学。 LCD代码的这种应用使人们对最小距离较大的LCD代码的构建产生了兴趣。我们还通过广义扭曲的芦苇固体代码提供了LCD MDS代码的新结构。
Maximum distance separable (MDS) codes are optimal where the minimum distance cannot be improved for a given length and code size. Twisted Reed-Solomon codes over finite fields were introduced in 2017, which are generalization of Reed-Solomon codes. Twisted Reed-Solomon codes can be applied in cryptography which prefer the codes with large minimum distance. MDS codes can be constructed from twisted Reed-Solomon codes, and most of them are not equivalent to Reed-Solomon codes. In this paper, we first generalize twisted Reed-Solomon codes to generalized twisted Reed-Solomon codes, then we give some new explicit constructions of MDS (generalized) twisted Reed-Solomon codes. In some cases, our constructions can get MDS codes with the length longer than the constructions of previous works. Linear complementary dual (LCD) codes are linear codes that intersect with their duals trivially. LCD codes can be applied in cryptography. This application of LCD codes renewed the interest in the construction of LCD codes having a large minimum distance. We also provide new constructions of LCD MDS codes from generalized twisted Reed-Solomon codes.
