论文标题
来自配对差异集的Grassmannian代码
Grassmannian codes from paired difference sets
论文作者
论文摘要
等缘紧密的框架（ETF）是希尔伯特空间中达到韦尔奇结合中平等的矢量序列，因此最小的一致性也是如此。更笼统地，纯正的紧密融合框架（ECTFF）是希尔伯特空间的一系列等维子空间，在Conway，Hardin和Sloane的单纯形上达到了平等。每种ECTFF都是一种最佳的Grassmannian代码，即Hilbert Space的Equi尺寸子空间的最佳包装。我们通过利用已知ETF之间的新关系来构建ECTFF。谐波ETF等于有限阿贝尔群体的差异集。我们说，当相应的谐波ETF的相应子序列恰好是其跨度的ETF时，这种组的差异设置为“配对”，其pontryagin dual设置为二元二元。我们表明，每对这样的一对都会产生ECTFF。此外，我们在两个元素的场上使用二次形式构建了一个无限的配对差异集。这共同产生了两个无限的真实ectff家族。
An equiangular tight frame (ETF) is a sequence of vectors in a Hilbert space that achieves equality in the Welch bound and so has minimal coherence. More generally, an equichordal tight fusion frame (ECTFF) is a sequence of equi-dimensional subspaces of a Hilbert space that achieves equality in Conway, Hardin and Sloane's simplex bound. Every ECTFF is a type of optimal Grassmannian code, that is, an optimal packing of equi-dimensional subspaces of a Hilbert space. We construct ECTFFs by exploiting new relationships between known ETFs. Harmonic ETFs equate to difference sets for finite abelian groups. We say that a difference set for such a group is "paired" with a difference set for its Pontryagin dual when the corresponding subsequence of its harmonic ETF happens to be an ETF for its span. We show that every such pair yields an ECTFF. We moreover construct an infinite family of paired difference sets using quadratic forms over the field of two elements. Together this yields two infinite families of real ECTFFs.
