论文标题
LCD子空间代码
LCD subspace codes
论文作者
论文摘要
子空间代码是向量空间$ \ MATHBB f^n_q $的非空间集。带有互补双重或LCD代码的线性代码是线性代码，其与双重的相交是微不足道的。在本文中，我们介绍了LCD子空间代码的概念。我们表明，LCD子空间代码的最小距离解码问题将减少到比通用子空间代码更简单的问题。此外，我们表明，在某些条件下，关联方案的公平分区产生了这样的LCD子空间代码，并且作为该方法的例证提供了一些示例。我们还通过相互无偏的Hadamard矩阵以及相互无偏的称重矩阵提供了一种结构。
A subspace code is a nonempty set of subspaces of a vector space $\mathbb F^n_q$. Linear codes with complementary duals, or LCD codes, are linear codes whose intersection with their duals is trivial. In this paper, we introduce a notion of LCD subspace codes. We show that the minimum distance decoding problem for an LCD subspace code reduces to a problem that is simpler than for a general subspace code. Further, we show that under some conditions equitable partitions of association schemes yield such LCD subspace codes and as an illustration of the method give some examples from distance-regular graphs. We also give a construction from mutually unbiased Hadamard matrices, and more generally, from mutually unbiased weighing matrices.
