Algebra Seminar

11/13/2019 - 2:00pm to 3:00pm
107 POT
Speaker(s) / Presenter(s): 
Hunter Lehmann, University of Kentucky
Title: Distance Distributions of Cyclic Orbit Codes
Abstract: Subspace codes are collections of subspaces of the finite vector space \mathbb{F}_q^n under the subspace metric. The distance distribution of such a code is the vector whose i^\text{th} entry counts the number of pairs of codewords with subspace distance i. Constant dimension cyclic orbit codes, which are contained in a Grassmannian \mathcal{G}_q(n,k) and are the orbit of a subspace under an action of \mathbb{F}_{q^n}^* on \mathcal{G}_q(n,k), are of particular interest. We show that for optimal such codes, the distance distribution depends only on q, n, and k. For more general codes, we can relate the distance distribution to the number of orbits which contain intersections between different codewords.
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