ALGB Seminar: Lisa Hernandez Lucas

05/03/2019 - 16:00

Title: Dimensional properties of SCIDs

Abstract: Consider a vector space V and a set of k-dimensional subspaces C = {π1,...,πn}. If these subspaces pairwise intersect in (k−t)-dimensional spaces, then C is called a (k,k−t)-SCID (set of Sub-spaces with Constant Intersection Dimension). When we identify the elements of C with codewords, this gives us in fact an equidistant sub-space code. The importance of SCIDs lies within random network coding, which can be illustrated with the butterfly network as an example.

For any SCID C we can define S:=〈π1,...,πn> and I:=〈πi∩πj | 1≤i < j≤n〉. Intuitively, when the space S has large dimension, the elements of C are further apart, causing the dimension of I being smaller and vice versa.

In this talk this intuition is justified by giving some upper bounds for dim S + dim I, and discussing which bounds are best for given parameters. On the other hand a spectrum result is presented, by constructing SCIDs for all possible values of dim S + dim I, under certain parameter conditions.